KILLED
proof of input_HqmGBV8WyP.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 0 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 0 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 11.4 s]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 62 ms]
    (18) typed CpxTrs
    (19) RewriteLemmaProof [LOWER BOUND(ID), 45 ms]
    (20) typed CpxTrs
    (21) RewriteLemmaProof [LOWER BOUND(ID), 2010 ms]
    (22) BEST
        (23) proven lower bound
            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
            (25) BOUNDS(n^1, INF)
        (26) typed CpxTrs
            (27) RewriteLemmaProof [LOWER BOUND(ID), 3531 ms]
            (28) typed CpxTrs
            (29) RewriteLemmaProof [LOWER BOUND(ID), 1838 ms]
            (30) typed CpxTrs
(31) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(32) CpxWeightedTrs
    (33) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CpxTypedWeightedTrs
    (35) CompletionProof [UPPER BOUND(ID), 0 ms]
    (36) CpxTypedWeightedCompleteTrs
        (37) NarrowingProof [BOTH BOUNDS(ID, ID), 24 ms]
        (38) CpxTypedWeightedCompleteTrs
        (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (40) CpxRNTS
        (41) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CpxRNTS
    (43) CompletionProof [UPPER BOUND(ID), 0 ms]
    (44) CpxTypedWeightedCompleteTrs
        (45) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
(47) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(48) CdtProblem
    (49) CdtLeafRemovalProof [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) NarrowingProof [BOTH BOUNDS(ID, ID), 3949 ms]
                (62) CpxTypedWeightedCompleteTrs
                (63) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (64) CpxRNTS
                (65) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (66) CpxRNTS
            (67) CompletionProof [UPPER BOUND(ID), 0 ms]
            (68) CpxTypedWeightedCompleteTrs
                (69) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms]
    (72) CdtProblem
        (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms]
        (88) CdtProblem
        (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (96) CdtProblem
        (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
        (114) CdtProblem
        (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms]
        (120) CdtProblem
        (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 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), 78 ms]
        (132) CdtProblem
        (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms]
        (138) CdtProblem
        (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
        (142) CdtProblem
        (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 70 ms]
        (146) CdtProblem
        (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms]
        (150) CdtProblem
        (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 154 ms]
        (154) CdtProblem
        (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms]
        (158) CdtProblem
        (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 139 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 161 ms]
        (166) CdtProblem
        (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 47 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 114 ms]
        (170) CdtProblem
        (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 240 ms]
        (174) CdtProblem
        (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 158 ms]
        (178) CdtProblem
        (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 250 ms]
        (182) CdtProblem
        (183) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 74 ms]
        (184) CdtProblem
        (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 36 ms]
        (186) CdtProblem
        (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 286 ms]
        (188) CdtProblem
        (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 57 ms]
        (190) CdtProblem
        (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
        (192) CdtProblem
        (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 235 ms]
        (194) CdtProblem
        (195) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 35 ms]
        (196) CdtProblem
        (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms]
        (198) CdtProblem
        (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 354 ms]
        (200) CdtProblem
        (201) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 27 ms]
        (202) CdtProblem
        (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 65 ms]
        (204) CdtProblem
        (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 247 ms]
        (206) CdtProblem
        (207) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 52 ms]
        (208) CdtProblem
        (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms]
        (210) CdtProblem
        (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 71 ms]
        (212) CdtProblem
        (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 340 ms]
        (214) CdtProblem
        (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 77 ms]
        (216) CdtProblem
        (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 225 ms]
        (218) CdtProblem
        (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 51 ms]
        (220) CdtProblem
        (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 298 ms]
        (222) CdtProblem
        (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 59 ms]
        (224) CdtProblem
        (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms]
        (226) CdtProblem
        (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 47 ms]
        (228) CdtProblem
        (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 190 ms]
        (230) CdtProblem
        (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 76 ms]
        (232) CdtProblem
        (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 205 ms]
        (234) CdtProblem
        (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 92 ms]
        (236) CdtProblem
        (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 158 ms]
        (238) CdtProblem
        (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 45 ms]
        (240) CdtProblem
        (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 220 ms]
        (242) CdtProblem
        (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 50 ms]
        (244) CdtProblem
        (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 338 ms]
        (246) CdtProblem
        (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms]
        (248) CdtProblem
        (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 313 ms]
        (250) CdtProblem
        (251) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms]
        (252) 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__p(0) -> 0
   a__p(s(X)) -> mark(X)
   a__leq(0, Y) -> true
   a__leq(s(X), 0) -> false
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y)))
   mark(p(X)) -> a__p(mark(X))
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
   mark(0) -> 0
   mark(s(X)) -> s(mark(X))
   mark(true) -> true
   mark(false) -> false
   a__p(X) -> p(X)
   a__leq(X1, X2) -> leq(X1, X2)
   a__if(X1, X2, X3) -> if(X1, X2, X3)
   a__diff(X1, X2) -> diff(X1, X2)

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

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

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


The TRS R consists of the following rules:

   a__p(0') -> 0'
   a__p(s(X)) -> mark(X)
   a__leq(0', Y) -> true
   a__leq(s(X), 0') -> false
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0', s(diff(p(X), Y)))
   mark(p(X)) -> a__p(mark(X))
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
   mark(0') -> 0'
   mark(s(X)) -> s(mark(X))
   mark(true) -> true
   mark(false) -> false
   a__p(X) -> p(X)
   a__leq(X1, X2) -> leq(X1, X2)
   a__if(X1, X2, X3) -> if(X1, X2, X3)
   a__diff(X1, X2) -> diff(X1, X2)

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

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

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


The TRS R consists of the following rules:

   a__p(0) -> 0
   a__p(s(X)) -> mark(X)
   a__leq(0, Y) -> true
   a__leq(s(X), 0) -> false
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y))
   a__if(true, X, Y) -> mark(X)
   a__if(false, X, Y) -> mark(Y)
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y)))
   mark(p(X)) -> a__p(mark(X))
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2))
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2))
   mark(0) -> 0
   mark(s(X)) -> s(mark(X))
   mark(true) -> true
   mark(false) -> false
   a__p(X) -> p(X)
   a__leq(X1, X2) -> leq(X1, X2)
   a__if(X1, X2, X3) -> if(X1, X2, X3)
   a__diff(X1, X2) -> diff(X1, X2)

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

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(0) -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0, z0) -> c3
   A__LEQ(s(z0), 0) -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0) -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23
S tuples:
   A__P(0) -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0, z0) -> c3
   A__LEQ(s(z0), 0) -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0) -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c, c1_1, c2, c3, c4, c5_2, c6_2, c7, c8_1, c9_1, c10, c11_3, c12_3, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20, c21_1, c22, c23


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

(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__P(0) -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0, z0) -> c3
   A__LEQ(s(z0), 0) -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0) -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23

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

   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false

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__P(0') -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0', z0) -> c3
   A__LEQ(s(z0), 0') -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0') -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23

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

   a__p(0') -> 0'
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0', z0) -> true
   a__leq(s(z0), 0') -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0') -> 0'
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false

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

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

(12)
Obligation:
Innermost TRS:
Rules:
A__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__P, MARK, A__LEQ, mark, A__IF, a__leq, a__p, a__if

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
mark < MARK
MARK = A__IF
a__leq < MARK
mark < A__LEQ
A__LEQ = A__IF
mark = a__leq
mark = a__p
mark = a__if
a__leq = a__p
a__leq = a__if
a__p = a__if

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

(14)
Obligation:
Innermost TRS:
Rules:
A__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
a__p, A__P, MARK, A__LEQ, mark, A__IF, a__leq, a__if

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
mark < MARK
MARK = A__IF
a__leq < MARK
mark < A__LEQ
A__LEQ = A__IF
mark = a__leq
mark = a__p
mark = a__if
a__leq = a__p
a__leq = a__if
a__p = a__if

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n10136_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n10136_24), rt in Omega(0)

Induction Base:
mark(gen_0':s:true:false:p:diff:leq:if7_24(0)) ->_R^Omega(0)
0'

Induction Step:
mark(gen_0':s:true:false:p:diff:leq:if7_24(+(n10136_24, 1))) ->_R^Omega(0)
s(mark(gen_0':s:true:false:p:diff:leq:if7_24(n10136_24))) ->_IH
s(gen_0':s:true:false:p:diff:leq:if7_24(c10137_24))

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__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n10136_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n10136_24), rt in Omega(0)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
a__leq, A__P, MARK, A__LEQ, A__IF, a__p, a__if

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
mark < MARK
MARK = A__IF
a__leq < MARK
mark < A__LEQ
A__LEQ = A__IF
mark = a__leq
mark = a__p
mark = a__if
a__leq = a__p
a__leq = a__if
a__p = a__if

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

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)

Induction Base:
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(0), gen_0':s:true:false:p:diff:leq:if7_24(0)) ->_R^Omega(0)
true

Induction Step:
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(+(n11751_24, 1)), gen_0':s:true:false:p:diff:leq:if7_24(+(n11751_24, 1))) ->_R^Omega(0)
a__leq(mark(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)), mark(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24))) ->_L^Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), mark(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24))) ->_L^Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) ->_IH
true

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__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n10136_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n10136_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
a__if, A__P, MARK, A__LEQ, mark, A__IF, a__p

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
mark < MARK
MARK = A__IF
a__leq < MARK
mark < A__LEQ
A__LEQ = A__IF
mark = a__leq
mark = a__p
mark = a__if
a__leq = a__p
a__leq = a__if
a__p = a__if

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

(19) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)

Induction Base:
mark(gen_0':s:true:false:p:diff:leq:if7_24(0)) ->_R^Omega(0)
0'

Induction Step:
mark(gen_0':s:true:false:p:diff:leq:if7_24(+(n13059_24, 1))) ->_R^Omega(0)
s(mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24))) ->_IH
s(gen_0':s:true:false:p:diff:leq:if7_24(c13060_24))

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__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
MARK, A__P, A__LEQ, A__IF

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
MARK = A__IF
A__LEQ = A__IF

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

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n14678_24))) -> *10_24, rt in Omega(n14678_24)

Induction Base:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, 0)))

Induction Step:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, +(n14678_24, 1)))) ->_R^Omega(1)
c21(MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n14678_24)))) ->_IH
c21(*10_24)

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__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
MARK, A__P, A__LEQ, A__IF

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
MARK = A__IF
A__LEQ = A__IF

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

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

(25)
BOUNDS(n^1, INF)

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

(26)
Obligation:
Innermost TRS:
Rules:
A__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n14678_24))) -> *10_24, rt in Omega(n14678_24)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
A__P, A__LEQ, A__IF

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
MARK = A__IF
A__LEQ = A__IF

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

(27) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24), gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)) -> *10_24, rt in Omega(n58186_24)

Induction Base:
A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(0), gen_0':s:true:false:p:diff:leq:if7_24(0))

Induction Step:
A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(+(n58186_24, 1)), gen_0':s:true:false:p:diff:leq:if7_24(+(n58186_24, 1))) ->_R^Omega(1)
c5(A__LEQ(mark(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)), mark(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24))), MARK(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24))) ->_L^Omega(0)
c5(A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24), mark(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24))), MARK(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24))) ->_L^Omega(0)
c5(A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24), gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)), MARK(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24))) ->_IH
c5(*10_24, MARK(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)))

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

(28)
Obligation:
Innermost TRS:
Rules:
A__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n14678_24))) -> *10_24, rt in Omega(n14678_24)
A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24), gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)) -> *10_24, rt in Omega(n58186_24)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
A__IF, A__P, MARK

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
MARK = A__IF
A__LEQ = A__IF

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

(29) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n132052_24))) -> *10_24, rt in Omega(n132052_24)

Induction Base:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, 0)))

Induction Step:
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, +(n132052_24, 1)))) ->_R^Omega(1)
c21(MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n132052_24)))) ->_IH
c21(*10_24)

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

(30)
Obligation:
Innermost TRS:
Rules:
A__P(0') -> c
A__P(s(z0)) -> c1(MARK(z0))
A__P(z0) -> c2
A__LEQ(0', z0) -> c3
A__LEQ(s(z0), 0') -> c4
A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__LEQ(z0, z1) -> c7
A__IF(true, z0, z1) -> c8(MARK(z0))
A__IF(false, z0, z1) -> c9(MARK(z1))
A__IF(z0, z1, z2) -> c10
A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
A__DIFF(z0, z1) -> c13
MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
MARK(0') -> c20
MARK(s(z0)) -> c21(MARK(z0))
MARK(true) -> c22
MARK(false) -> c23
a__p(0') -> 0'
a__p(s(z0)) -> mark(z0)
a__p(z0) -> p(z0)
a__leq(0', z0) -> true
a__leq(s(z0), 0') -> false
a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
a__leq(z0, z1) -> leq(z0, z1)
a__if(true, z0, z1) -> mark(z0)
a__if(false, z0, z1) -> mark(z1)
a__if(z0, z1, z2) -> if(z0, z1, z2)
a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0', s(diff(p(z0), z1)))
a__diff(z0, z1) -> diff(z0, z1)
mark(p(z0)) -> a__p(mark(z0))
mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
mark(0') -> 0'
mark(s(z0)) -> s(mark(z0))
mark(true) -> true
mark(false) -> false

Types:
A__P :: 0':s:true:false:p:diff:leq:if -> c:c1:c2
0' :: 0':s:true:false:p:diff:leq:if
c :: c:c1:c2
s :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c:c1:c2
MARK :: 0':s:true:false:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c2 :: c:c1:c2
A__LEQ :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c3:c4:c5:c6:c7
c3 :: c3:c4:c5:c6:c7
c4 :: c3:c4:c5:c6:c7
c5 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
mark :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c6 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c3:c4:c5:c6:c7
c7 :: c3:c4:c5:c6:c7
A__IF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c8:c9:c10
true :: 0':s:true:false:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
false :: 0':s:true:false:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c8:c9:c10
c10 :: c8:c9:c10
A__DIFF :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> c11:c12:c13
c11 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
a__leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c12 :: c8:c9:c10 -> c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c:c1:c2 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
leq :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c15 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c16 :: c3:c4:c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c18 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
a__p :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__if :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
a__diff :: 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if -> 0':s:true:false:p:diff:leq:if
hole_c:c1:c21_24 :: c:c1:c2
hole_0':s:true:false:p:diff:leq:if2_24 :: 0':s:true:false:p:diff:leq:if
hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c233_24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
hole_c3:c4:c5:c6:c74_24 :: c3:c4:c5:c6:c7
hole_c8:c9:c105_24 :: c8:c9:c10
hole_c11:c12:c136_24 :: c11:c12:c13
gen_0':s:true:false:p:diff:leq:if7_24 :: Nat -> 0':s:true:false:p:diff:leq:if
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23
gen_c3:c4:c5:c6:c79_24 :: Nat -> c3:c4:c5:c6:c7


Lemmas:
mark(gen_0':s:true:false:p:diff:leq:if7_24(n13059_24)) -> gen_0':s:true:false:p:diff:leq:if7_24(n13059_24), rt in Omega(0)
a__leq(gen_0':s:true:false:p:diff:leq:if7_24(n11751_24), gen_0':s:true:false:p:diff:leq:if7_24(n11751_24)) -> true, rt in Omega(0)
MARK(gen_0':s:true:false:p:diff:leq:if7_24(+(1, n132052_24))) -> *10_24, rt in Omega(n132052_24)
A__LEQ(gen_0':s:true:false:p:diff:leq:if7_24(n58186_24), gen_0':s:true:false:p:diff:leq:if7_24(n58186_24)) -> *10_24, rt in Omega(n58186_24)


Generator Equations:
gen_0':s:true:false:p:diff:leq:if7_24(0) <=> 0'
gen_0':s:true:false:p:diff:leq:if7_24(+(x, 1)) <=> s(gen_0':s:true:false:p:diff:leq:if7_24(x))
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(0) <=> c20
gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(+(x, 1)) <=> c14(c, gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c238_24(x))
gen_c3:c4:c5:c6:c79_24(0) <=> c3
gen_c3:c4:c5:c6:c79_24(+(x, 1)) <=> c5(gen_c3:c4:c5:c6:c79_24(x), c20)


The following defined symbols remain to be analysed:
A__P

They will be analysed ascendingly in the following order:
A__P = MARK
A__P = A__LEQ
A__P = A__IF
MARK = A__LEQ
MARK = A__IF
A__LEQ = A__IF

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

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

(32)
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__p(0) -> 0 [1]
   a__p(s(X)) -> mark(X) [1]
   a__leq(0, Y) -> true [1]
   a__leq(s(X), 0) -> false [1]
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) [1]
   mark(p(X)) -> a__p(mark(X)) [1]
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1]
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__p(X) -> p(X) [1]
   a__leq(X1, X2) -> leq(X1, X2) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]
   a__diff(X1, X2) -> diff(X1, X2) [1]

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

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

(34)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__p(0) -> 0 [1]
   a__p(s(X)) -> mark(X) [1]
   a__leq(0, Y) -> true [1]
   a__leq(s(X), 0) -> false [1]
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) [1]
   mark(p(X)) -> a__p(mark(X)) [1]
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1]
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__p(X) -> p(X) [1]
   a__leq(X1, X2) -> leq(X1, X2) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]
   a__diff(X1, X2) -> diff(X1, X2) [1]

The TRS has the following type information:
a__p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
0 :: 0:s:true:false:p:diff:leq:if
s :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
mark :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
true :: 0:s:true:false:p:diff:leq:if
false :: 0:s:true:false:p:diff:leq:if
a__if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if

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

(35) 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__leq_2
   a__if_3
   a__p_1
   a__diff_2

Due to the following rules being added:
none

And the following fresh constants: none

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

(36)
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__p(0) -> 0 [1]
   a__p(s(X)) -> mark(X) [1]
   a__leq(0, Y) -> true [1]
   a__leq(s(X), 0) -> false [1]
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) [1]
   mark(p(X)) -> a__p(mark(X)) [1]
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1]
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__p(X) -> p(X) [1]
   a__leq(X1, X2) -> leq(X1, X2) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]
   a__diff(X1, X2) -> diff(X1, X2) [1]

The TRS has the following type information:
a__p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
0 :: 0:s:true:false:p:diff:leq:if
s :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
mark :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
true :: 0:s:true:false:p:diff:leq:if
false :: 0:s:true:false:p:diff:leq:if
a__if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if

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

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

(38)
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__p(0) -> 0 [1]
   a__p(s(X)) -> mark(X) [1]
   a__leq(0, Y) -> true [1]
   a__leq(s(X), 0) -> false [1]
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) [1]
   mark(p(p(X61))) -> a__p(a__p(mark(X61))) [2]
   mark(p(leq(X153, X253))) -> a__p(a__leq(mark(X153), mark(X253))) [2]
   mark(p(if(X154, X254, X321))) -> a__p(a__if(mark(X154), X254, X321)) [2]
   mark(p(diff(X155, X255))) -> a__p(a__diff(mark(X155), mark(X255))) [2]
   mark(p(0)) -> a__p(0) [2]
   mark(p(s(X62))) -> a__p(s(mark(X62))) [2]
   mark(p(true)) -> a__p(true) [2]
   mark(p(false)) -> a__p(false) [2]
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) [1]
   mark(if(p(X81), X2, X3)) -> a__if(a__p(mark(X81)), X2, X3) [2]
   mark(if(leq(X183, X283), X2, X3)) -> a__if(a__leq(mark(X183), mark(X283)), X2, X3) [2]
   mark(if(if(X184, X284, X331), X2, X3)) -> a__if(a__if(mark(X184), X284, X331), X2, X3) [2]
   mark(if(diff(X185, X285), X2, X3)) -> a__if(a__diff(mark(X185), mark(X285)), X2, X3) [2]
   mark(if(0, X2, X3)) -> a__if(0, X2, X3) [2]
   mark(if(s(X82), X2, X3)) -> a__if(s(mark(X82)), X2, X3) [2]
   mark(if(true, X2, X3)) -> a__if(true, X2, X3) [2]
   mark(if(false, X2, X3)) -> a__if(false, X2, X3) [2]
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__p(X) -> p(X) [1]
   a__leq(X1, X2) -> leq(X1, X2) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]
   a__diff(X1, X2) -> diff(X1, X2) [1]

The TRS has the following type information:
a__p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
0 :: 0:s:true:false:p:diff:leq:if
s :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
mark :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
true :: 0:s:true:false:p:diff:leq:if
false :: 0:s:true:false:p:diff:leq:if
a__if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if

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

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

   0 => 0
   true => 2
   false => 1

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

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

   a__diff(z, z') -{ 1 }-> a__if(a__leq(mark(X), mark(Y)), 0, 1 + (1 + (1 + X) + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X
   a__diff(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__leq(z, z') -{ 1 }-> a__leq(mark(X), mark(Y)) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   a__leq(z, z') -{ 1 }-> 2 :|: z' = Y, Y >= 0, z = 0
   a__leq(z, z') -{ 1 }-> 1 :|: z = 1 + X, X >= 0, z' = 0
   a__leq(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__p(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0
   a__p(z) -{ 1 }-> 0 :|: z = 0
   a__p(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   mark(z) -{ 2 }-> a__p(a__p(mark(X61))) :|: X61 >= 0, z = 1 + (1 + X61)
   mark(z) -{ 2 }-> a__p(a__leq(mark(X153), mark(X253))) :|: z = 1 + (1 + X153 + X253), X253 >= 0, X153 >= 0
   mark(z) -{ 2 }-> a__p(a__if(mark(X154), X254, X321)) :|: X321 >= 0, X154 >= 0, X254 >= 0, z = 1 + (1 + X154 + X254 + X321)
   mark(z) -{ 2 }-> a__p(a__diff(mark(X155), mark(X255))) :|: X255 >= 0, X155 >= 0, z = 1 + (1 + X155 + X255)
   mark(z) -{ 2 }-> a__p(2) :|: z = 1 + 2
   mark(z) -{ 2 }-> a__p(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__p(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__p(1 + mark(X62)) :|: X62 >= 0, z = 1 + (1 + X62)
   mark(z) -{ 1 }-> a__leq(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__if(a__p(mark(X81)), X2, X3) :|: z = 1 + (1 + X81) + X2 + X3, X81 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(a__leq(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3
   mark(z) -{ 2 }-> a__if(a__if(mark(X184), X284, X331), X2, X3) :|: z = 1 + (1 + X184 + X284 + X331) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X331 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(a__diff(mark(X185), mark(X285)), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__if(2, X2, X3) :|: z = 1 + 2 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(1 + mark(X82), X2, X3) :|: z = 1 + (1 + X82) + X2 + X3, X82 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 1 }-> a__diff(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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

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

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

   a__diff(z, z') -{ 1 }-> a__if(a__leq(mark(z), mark(z')), 0, 1 + (1 + (1 + z) + z')) :|: z' >= 0, z >= 0
   a__diff(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__if(z, z', z'') -{ 1 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0
   a__if(z, z', z'') -{ 1 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__leq(z, z') -{ 1 }-> a__leq(mark(z - 1), mark(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   a__leq(z, z') -{ 1 }-> 2 :|: z' >= 0, z = 0
   a__leq(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0
   a__leq(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__p(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0
   a__p(z) -{ 1 }-> 0 :|: z = 0
   a__p(z) -{ 1 }-> 1 + z :|: z >= 0
   mark(z) -{ 2 }-> a__p(a__p(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__p(a__leq(mark(X153), mark(X253))) :|: z = 1 + (1 + X153 + X253), X253 >= 0, X153 >= 0
   mark(z) -{ 2 }-> a__p(a__if(mark(X154), X254, X321)) :|: X321 >= 0, X154 >= 0, X254 >= 0, z = 1 + (1 + X154 + X254 + X321)
   mark(z) -{ 2 }-> a__p(a__diff(mark(X155), mark(X255))) :|: X255 >= 0, X155 >= 0, z = 1 + (1 + X155 + X255)
   mark(z) -{ 2 }-> a__p(2) :|: z = 1 + 2
   mark(z) -{ 2 }-> a__p(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__p(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__p(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 1 }-> a__leq(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__if(a__p(mark(X81)), X2, X3) :|: z = 1 + (1 + X81) + X2 + X3, X81 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(a__leq(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3
   mark(z) -{ 2 }-> a__if(a__if(mark(X184), X284, X331), X2, X3) :|: z = 1 + (1 + X184 + X284 + X331) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X331 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(a__diff(mark(X185), mark(X285)), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__if(2, X2, X3) :|: z = 1 + 2 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__if(1 + mark(X82), X2, X3) :|: z = 1 + (1 + X82) + X2 + X3, X82 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 1 }-> a__diff(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

(43) 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

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

(44)
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__p(0) -> 0 [1]
   a__p(s(X)) -> mark(X) [1]
   a__leq(0, Y) -> true [1]
   a__leq(s(X), 0) -> false [1]
   a__leq(s(X), s(Y)) -> a__leq(mark(X), mark(Y)) [1]
   a__if(true, X, Y) -> mark(X) [1]
   a__if(false, X, Y) -> mark(Y) [1]
   a__diff(X, Y) -> a__if(a__leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) [1]
   mark(p(X)) -> a__p(mark(X)) [1]
   mark(leq(X1, X2)) -> a__leq(mark(X1), mark(X2)) [1]
   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3) [1]
   mark(diff(X1, X2)) -> a__diff(mark(X1), mark(X2)) [1]
   mark(0) -> 0 [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(true) -> true [1]
   mark(false) -> false [1]
   a__p(X) -> p(X) [1]
   a__leq(X1, X2) -> leq(X1, X2) [1]
   a__if(X1, X2, X3) -> if(X1, X2, X3) [1]
   a__diff(X1, X2) -> diff(X1, X2) [1]

The TRS has the following type information:
a__p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
0 :: 0:s:true:false:p:diff:leq:if
s :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
mark :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
true :: 0:s:true:false:p:diff:leq:if
false :: 0:s:true:false:p:diff:leq:if
a__if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
a__diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
diff :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
p :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
leq :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if
if :: 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if -> 0:s:true:false:p:diff:leq:if

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

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

   0 => 0
   true => 2
   false => 1

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

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   a__diff(z, z') -{ 1 }-> a__if(a__leq(mark(X), mark(Y)), 0, 1 + (1 + (1 + X) + Y)) :|: z' = Y, Y >= 0, X >= 0, z = X
   a__diff(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__if(z, z', z'') -{ 1 }-> mark(X) :|: z = 2, z' = X, Y >= 0, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> mark(Y) :|: z' = X, Y >= 0, z = 1, z'' = Y, X >= 0
   a__if(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__leq(z, z') -{ 1 }-> a__leq(mark(X), mark(Y)) :|: z = 1 + X, Y >= 0, z' = 1 + Y, X >= 0
   a__leq(z, z') -{ 1 }-> 2 :|: z' = Y, Y >= 0, z = 0
   a__leq(z, z') -{ 1 }-> 1 :|: z = 1 + X, X >= 0, z' = 0
   a__leq(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__p(z) -{ 1 }-> mark(X) :|: z = 1 + X, X >= 0
   a__p(z) -{ 1 }-> 0 :|: z = 0
   a__p(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   mark(z) -{ 1 }-> a__p(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__leq(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__if(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__diff(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 2 :|: z = 2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(0) -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0, z0) -> c3
   A__LEQ(s(z0), 0) -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0) -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23
S tuples:
   A__P(0) -> c
   A__P(s(z0)) -> c1(MARK(z0))
   A__P(z0) -> c2
   A__LEQ(0, z0) -> c3
   A__LEQ(s(z0), 0) -> c4
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__LEQ(z0, z1) -> c7
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__IF(z0, z1, z2) -> c10
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__DIFF(z0, z1) -> c13
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(0) -> c20
   MARK(s(z0)) -> c21(MARK(z0))
   MARK(true) -> c22
   MARK(false) -> c23
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c, c1_1, c2, c3, c4, c5_2, c6_2, c7, c8_1, c9_1, c10, c11_3, c12_3, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20, c21_1, c22, c23


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

(49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   MARK(false) -> c23
   A__LEQ(0, z0) -> c3
   A__P(z0) -> c2
   A__DIFF(z0, z1) -> c13
   A__IF(z0, z1, z2) -> c10
   A__LEQ(s(z0), 0) -> c4
   A__P(0) -> c
   MARK(true) -> c22
   A__LEQ(z0, z1) -> c7
   MARK(0) -> c20

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c1_1, c5_2, c6_2, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_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__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))

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

   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false

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__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false

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__P(s(z0)) -> c1(MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   A__IF(true, z0, z1) -> c8(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c9(MARK(z1)) [1]
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c21(MARK(z0)) [1]
   a__p(0) -> 0 [0]
   a__p(s(z0)) -> mark(z0) [0]
   a__p(z0) -> p(z0) [0]
   a__leq(0, z0) -> true [0]
   a__leq(s(z0), 0) -> false [0]
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1)) [0]
   a__leq(z0, z1) -> leq(z0, z1) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))) [0]
   a__diff(z0, z1) -> diff(z0, z1) [0]
   mark(p(z0)) -> a__p(mark(z0)) [0]
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0]
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1)) [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(true) -> true [0]
   mark(false) -> false [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__P(s(z0)) -> c1(MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   A__IF(true, z0, z1) -> c8(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c9(MARK(z1)) [1]
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c21(MARK(z0)) [1]
   a__p(0) -> 0 [0]
   a__p(s(z0)) -> mark(z0) [0]
   a__p(z0) -> p(z0) [0]
   a__leq(0, z0) -> true [0]
   a__leq(s(z0), 0) -> false [0]
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1)) [0]
   a__leq(z0, z1) -> leq(z0, z1) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))) [0]
   a__diff(z0, z1) -> diff(z0, z1) [0]
   mark(p(z0)) -> a__p(mark(z0)) [0]
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0]
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1)) [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(true) -> true [0]
   mark(false) -> false [0]

The TRS has the following type information:
A__P :: s:true:false:0:p:diff:leq:if -> c1
s :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
c1 :: c14:c15:c16:c17:c18:c19:c21 -> c1
MARK :: s:true:false:0:p:diff:leq:if -> c14:c15:c16:c17:c18:c19:c21
A__LEQ :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> c5:c6
c5 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
mark :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
c6 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
A__IF :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> c8:c9
true :: s:true:false:0:p:diff:leq:if
c8 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
false :: s:true:false:0:p:diff:leq:if
c9 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
A__DIFF :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> c11:c12
c11 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
a__leq :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
0 :: s:true:false:0:p:diff:leq:if
diff :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
p :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
c12 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
c14 :: c1 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
leq :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
c15 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c16 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
if :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
c17 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c18 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c19 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
a__p :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
a__if :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if
a__diff :: s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if -> s:true:false:0:p:diff:leq:if

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__P_1
   A__LEQ_2
   A__IF_3
   A__DIFF_2
   MARK_1

(c) The following functions are completely defined:

   a__p_1
   a__leq_2
   a__if_3
   a__diff_2
   mark_1

Due to the following rules being added:

   a__p(v0) -> null_a__p [0]
   a__leq(v0, v1) -> null_a__leq [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   a__diff(v0, v1) -> null_a__diff [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__p, null_a__leq, null_a__if, null_a__diff, null_mark, const, const1, const2, const3, const4

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

(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__P(s(z0)) -> c1(MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   A__IF(true, z0, z1) -> c8(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c9(MARK(z1)) [1]
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c21(MARK(z0)) [1]
   a__p(0) -> 0 [0]
   a__p(s(z0)) -> mark(z0) [0]
   a__p(z0) -> p(z0) [0]
   a__leq(0, z0) -> true [0]
   a__leq(s(z0), 0) -> false [0]
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1)) [0]
   a__leq(z0, z1) -> leq(z0, z1) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))) [0]
   a__diff(z0, z1) -> diff(z0, z1) [0]
   mark(p(z0)) -> a__p(mark(z0)) [0]
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0]
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1)) [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__p(v0) -> null_a__p [0]
   a__leq(v0, v1) -> null_a__leq [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   a__diff(v0, v1) -> null_a__diff [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__P :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c1
s :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c1 :: c14:c15:c16:c17:c18:c19:c21 -> c1
MARK :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c14:c15:c16:c17:c18:c19:c21
A__LEQ :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c5:c6
c5 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c6 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
A__IF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c8:c9
true :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c8 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
false :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c9 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
A__DIFF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c11:c12
c11 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
0 :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c12 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
c14 :: c1 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c15 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c16 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c17 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c18 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c19 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
const :: c1
const1 :: c14:c15:c16:c17:c18:c19:c21
const2 :: c5:c6
const3 :: c8:c9
const4 :: c11:c12

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

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

(62)
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__P(s(z0)) -> c1(MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   A__IF(true, z0, z1) -> c8(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c9(MARK(z1)) [1]
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(p(p(z0539))) -> c14(A__P(a__p(mark(z0539))), MARK(p(z0539))) [1]
   MARK(p(leq(z0540, z1323))) -> c14(A__P(a__leq(mark(z0540), mark(z1323))), MARK(leq(z0540, z1323))) [1]
   MARK(p(if(z0541, z1324, z2107))) -> c14(A__P(a__if(mark(z0541), z1324, z2107)), MARK(if(z0541, z1324, z2107))) [1]
   MARK(p(diff(z0542, z1325))) -> c14(A__P(a__diff(mark(z0542), mark(z1325))), MARK(diff(z0542, z1325))) [1]
   MARK(p(0)) -> c14(A__P(0), MARK(0)) [1]
   MARK(p(s(z0543))) -> c14(A__P(s(mark(z0543))), MARK(s(z0543))) [1]
   MARK(p(true)) -> c14(A__P(true), MARK(true)) [1]
   MARK(p(false)) -> c14(A__P(false), MARK(false)) [1]
   MARK(p(z0)) -> c14(A__P(null_mark), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(if(p(z0644), z1, z2)) -> c17(A__IF(a__p(mark(z0644)), z1, z2), MARK(p(z0644))) [1]
   MARK(if(leq(z0645, z1386), z1, z2)) -> c17(A__IF(a__leq(mark(z0645), mark(z1386)), z1, z2), MARK(leq(z0645, z1386))) [1]
   MARK(if(if(z0646, z1387, z2128), z1, z2)) -> c17(A__IF(a__if(mark(z0646), z1387, z2128), z1, z2), MARK(if(z0646, z1387, z2128))) [1]
   MARK(if(diff(z0647, z1388), z1, z2)) -> c17(A__IF(a__diff(mark(z0647), mark(z1388)), z1, z2), MARK(diff(z0647, z1388))) [1]
   MARK(if(0, z1, z2)) -> c17(A__IF(0, z1, z2), MARK(0)) [1]
   MARK(if(s(z0648), z1, z2)) -> c17(A__IF(s(mark(z0648)), z1, z2), MARK(s(z0648))) [1]
   MARK(if(true, z1, z2)) -> c17(A__IF(true, z1, z2), MARK(true)) [1]
   MARK(if(false, z1, z2)) -> c17(A__IF(false, z1, z2), MARK(false)) [1]
   MARK(if(z0, z1, z2)) -> c17(A__IF(null_mark, z1, z2), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c21(MARK(z0)) [1]
   a__p(0) -> 0 [0]
   a__p(s(z0)) -> mark(z0) [0]
   a__p(z0) -> p(z0) [0]
   a__leq(0, z0) -> true [0]
   a__leq(s(z0), 0) -> false [0]
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1)) [0]
   a__leq(z0, z1) -> leq(z0, z1) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))) [0]
   a__diff(z0, z1) -> diff(z0, z1) [0]
   mark(p(p(z0849))) -> a__p(a__p(mark(z0849))) [0]
   mark(p(leq(z0850, z1509))) -> a__p(a__leq(mark(z0850), mark(z1509))) [0]
   mark(p(if(z0851, z1510, z2169))) -> a__p(a__if(mark(z0851), z1510, z2169)) [0]
   mark(p(diff(z0852, z1511))) -> a__p(a__diff(mark(z0852), mark(z1511))) [0]
   mark(p(0)) -> a__p(0) [0]
   mark(p(s(z0853))) -> a__p(s(mark(z0853))) [0]
   mark(p(true)) -> a__p(true) [0]
   mark(p(false)) -> a__p(false) [0]
   mark(p(z0)) -> a__p(null_mark) [0]
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1)) [0]
   mark(if(p(z0904), z1, z2)) -> a__if(a__p(mark(z0904)), z1, z2) [0]
   mark(if(leq(z0905, z1542), z1, z2)) -> a__if(a__leq(mark(z0905), mark(z1542)), z1, z2) [0]
   mark(if(if(z0906, z1543, z2180), z1, z2)) -> a__if(a__if(mark(z0906), z1543, z2180), z1, z2) [0]
   mark(if(diff(z0907, z1544), z1, z2)) -> a__if(a__diff(mark(z0907), mark(z1544)), z1, z2) [0]
   mark(if(0, z1, z2)) -> a__if(0, z1, z2) [0]
   mark(if(s(z0908), z1, z2)) -> a__if(s(mark(z0908)), z1, z2) [0]
   mark(if(true, z1, z2)) -> a__if(true, z1, z2) [0]
   mark(if(false, z1, z2)) -> a__if(false, z1, z2) [0]
   mark(if(z0, z1, z2)) -> a__if(null_mark, z1, z2) [0]
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1)) [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__p(v0) -> null_a__p [0]
   a__leq(v0, v1) -> null_a__leq [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   a__diff(v0, v1) -> null_a__diff [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__P :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c1
s :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c1 :: c14:c15:c16:c17:c18:c19:c21 -> c1
MARK :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c14:c15:c16:c17:c18:c19:c21
A__LEQ :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c5:c6
c5 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c6 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c5:c6
A__IF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c8:c9
true :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c8 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
false :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c9 :: c14:c15:c16:c17:c18:c19:c21 -> c8:c9
A__DIFF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c11:c12
c11 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
0 :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c12 :: c8:c9 -> c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c11:c12
c14 :: c1 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c15 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c16 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c17 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c18 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c19 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21
a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
const :: c1
const1 :: c14:c15:c16:c17:c18:c19:c21
const2 :: c5:c6
const3 :: c8:c9
const4 :: c11:c12

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:

   true => 2
   false => 1
   0 => 0
   null_a__p => 0
   null_a__leq => 0
   null_a__if => 0
   null_a__diff => 0
   null_mark => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0

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

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

   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   A__P(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__p(mark(z0539))) + MARK(1 + z0539) :|: z = 1 + (1 + z0539), z0539 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__leq(mark(z0540), mark(z1323))) + MARK(1 + z0540 + z1323) :|: z = 1 + (1 + z0540 + z1323), z1323 >= 0, z0540 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__if(mark(z0541), z1324, z2107)) + MARK(1 + z0541 + z1324 + z2107) :|: z2107 >= 0, z1324 >= 0, z = 1 + (1 + z0541 + z1324 + z2107), z0541 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__diff(mark(z0542), mark(z1325))) + MARK(1 + z0542 + z1325) :|: z0542 >= 0, z1325 >= 0, z = 1 + (1 + z0542 + z1325)
   MARK(z) -{ 1 }-> 1 + A__P(2) + MARK(2) :|: z = 1 + 2
   MARK(z) -{ 1 }-> 1 + A__P(1) + MARK(1) :|: z = 1 + 1
   MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(0) :|: z = 1 + 0
   MARK(z) -{ 1 }-> 1 + A__P(1 + mark(z0543)) + MARK(1 + z0543) :|: z0543 >= 0, z = 1 + (1 + z0543)
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__IF(a__p(mark(z0644)), z1, z2) + MARK(1 + z0644) :|: z1 >= 0, z0644 >= 0, z = 1 + (1 + z0644) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__leq(mark(z0645), mark(z1386)), z1, z2) + MARK(1 + z0645 + z1386) :|: z0645 >= 0, z1 >= 0, z = 1 + (1 + z0645 + z1386) + z1 + z2, z2 >= 0, z1386 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__if(mark(z0646), z1387, z2128), z1, z2) + MARK(1 + z0646 + z1387 + z2128) :|: z1 >= 0, z = 1 + (1 + z0646 + z1387 + z2128) + z1 + z2, z2128 >= 0, z0646 >= 0, z1387 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__diff(mark(z0647), mark(z1388)), z1, z2) + MARK(1 + z0647 + z1388) :|: z1 >= 0, z1388 >= 0, z = 1 + (1 + z0647 + z1388) + z1 + z2, z0647 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(2, z1, z2) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(1 + mark(z0648), z1, z2) + MARK(1 + z0648) :|: z = 1 + (1 + z0648) + z1 + z2, z1 >= 0, z0648 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__diff(z, z') -{ 0 }-> a__if(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__diff(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__diff(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__leq(z, z') -{ 0 }-> a__leq(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   a__leq(z, z') -{ 0 }-> 2 :|: z0 >= 0, z = 0, z' = z0
   a__leq(z, z') -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   a__leq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__leq(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__p(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0
   a__p(z) -{ 0 }-> 0 :|: z = 0
   a__p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__p(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   mark(z) -{ 0 }-> a__p(a__p(mark(z0849))) :|: z = 1 + (1 + z0849), z0849 >= 0
   mark(z) -{ 0 }-> a__p(a__leq(mark(z0850), mark(z1509))) :|: z0850 >= 0, z = 1 + (1 + z0850 + z1509), z1509 >= 0
   mark(z) -{ 0 }-> a__p(a__if(mark(z0851), z1510, z2169)) :|: z = 1 + (1 + z0851 + z1510 + z2169), z0851 >= 0, z1510 >= 0, z2169 >= 0
   mark(z) -{ 0 }-> a__p(a__diff(mark(z0852), mark(z1511))) :|: z0852 >= 0, z1511 >= 0, z = 1 + (1 + z0852 + z1511)
   mark(z) -{ 0 }-> a__p(2) :|: z = 1 + 2
   mark(z) -{ 0 }-> a__p(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__p(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__p(0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__p(1 + mark(z0853)) :|: z0853 >= 0, z = 1 + (1 + z0853)
   mark(z) -{ 0 }-> a__leq(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__if(a__p(mark(z0904)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0904) + z1 + z2, z2 >= 0, z0904 >= 0
   mark(z) -{ 0 }-> a__if(a__leq(mark(z0905), mark(z1542)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0905 + z1542) + z1 + z2, z1542 >= 0, z0905 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(a__if(mark(z0906), z1543, z2180), z1, z2) :|: z = 1 + (1 + z0906 + z1543 + z2180) + z1 + z2, z1 >= 0, z2180 >= 0, z0906 >= 0, z1543 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(a__diff(mark(z0907), mark(z1544)), z1, z2) :|: z1 >= 0, z0907 >= 0, z = 1 + (1 + z0907 + z1544) + z1 + z2, z2 >= 0, z1544 >= 0
   mark(z) -{ 0 }-> a__if(2, z1, z2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(1 + mark(z0908), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0908) + z1 + z2, z0908 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__diff(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0


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

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

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

   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z), mark(z')), 0, 1 + (1 + (1 + z) + z')) + A__LEQ(mark(z), mark(z')) + MARK(z) :|: z' >= 0, z >= 0
   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z), mark(z')), 0, 1 + (1 + (1 + z) + z')) + A__LEQ(mark(z), mark(z')) + MARK(z') :|: z' >= 0, z >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z') :|: z = 2, z'' >= 0, z' >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z - 1), mark(z' - 1)) + MARK(z - 1) :|: z' - 1 >= 0, z - 1 >= 0
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z - 1), mark(z' - 1)) + MARK(z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   A__P(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__p(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__leq(mark(z0540), mark(z1323))) + MARK(1 + z0540 + z1323) :|: z = 1 + (1 + z0540 + z1323), z1323 >= 0, z0540 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__if(mark(z0541), z1324, z2107)) + MARK(1 + z0541 + z1324 + z2107) :|: z2107 >= 0, z1324 >= 0, z = 1 + (1 + z0541 + z1324 + z2107), z0541 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(a__diff(mark(z0542), mark(z1325))) + MARK(1 + z0542 + z1325) :|: z0542 >= 0, z1325 >= 0, z = 1 + (1 + z0542 + z1325)
   MARK(z) -{ 1 }-> 1 + A__P(2) + MARK(2) :|: z = 1 + 2
   MARK(z) -{ 1 }-> 1 + A__P(1) + MARK(1) :|: z = 1 + 1
   MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(0) :|: z = 1 + 0
   MARK(z) -{ 1 }-> 1 + A__P(0) + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__IF(a__p(mark(z0644)), z1, z2) + MARK(1 + z0644) :|: z1 >= 0, z0644 >= 0, z = 1 + (1 + z0644) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__leq(mark(z0645), mark(z1386)), z1, z2) + MARK(1 + z0645 + z1386) :|: z0645 >= 0, z1 >= 0, z = 1 + (1 + z0645 + z1386) + z1 + z2, z2 >= 0, z1386 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__if(mark(z0646), z1387, z2128), z1, z2) + MARK(1 + z0646 + z1387 + z2128) :|: z1 >= 0, z = 1 + (1 + z0646 + z1387 + z2128) + z1 + z2, z2128 >= 0, z0646 >= 0, z1387 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(a__diff(mark(z0647), mark(z1388)), z1, z2) + MARK(1 + z0647 + z1388) :|: z1 >= 0, z1388 >= 0, z = 1 + (1 + z0647 + z1388) + z1 + z2, z0647 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(2, z1, z2) + MARK(2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__IF(1 + mark(z0648), z1, z2) + MARK(1 + z0648) :|: z = 1 + (1 + z0648) + z1 + z2, z1 >= 0, z0648 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__diff(z, z') -{ 0 }-> a__if(a__leq(mark(z), mark(z')), 0, 1 + (1 + (1 + z) + z')) :|: z' >= 0, z >= 0
   a__diff(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__diff(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z') :|: z = 2, z'' >= 0, z' >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z'') :|: z'' >= 0, z = 1, z' >= 0
   a__if(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__leq(z, z') -{ 0 }-> a__leq(mark(z - 1), mark(z' - 1)) :|: z' - 1 >= 0, z - 1 >= 0
   a__leq(z, z') -{ 0 }-> 2 :|: z' >= 0, z = 0
   a__leq(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0
   a__leq(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__leq(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__p(z) -{ 0 }-> mark(z - 1) :|: z - 1 >= 0
   a__p(z) -{ 0 }-> 0 :|: z = 0
   a__p(z) -{ 0 }-> 0 :|: z >= 0
   a__p(z) -{ 0 }-> 1 + z :|: z >= 0
   mark(z) -{ 0 }-> a__p(a__p(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__p(a__leq(mark(z0850), mark(z1509))) :|: z0850 >= 0, z = 1 + (1 + z0850 + z1509), z1509 >= 0
   mark(z) -{ 0 }-> a__p(a__if(mark(z0851), z1510, z2169)) :|: z = 1 + (1 + z0851 + z1510 + z2169), z0851 >= 0, z1510 >= 0, z2169 >= 0
   mark(z) -{ 0 }-> a__p(a__diff(mark(z0852), mark(z1511))) :|: z0852 >= 0, z1511 >= 0, z = 1 + (1 + z0852 + z1511)
   mark(z) -{ 0 }-> a__p(2) :|: z = 1 + 2
   mark(z) -{ 0 }-> a__p(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__p(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__p(0) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__p(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__leq(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__if(a__p(mark(z0904)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0904) + z1 + z2, z2 >= 0, z0904 >= 0
   mark(z) -{ 0 }-> a__if(a__leq(mark(z0905), mark(z1542)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0905 + z1542) + z1 + z2, z1542 >= 0, z0905 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(a__if(mark(z0906), z1543, z2180), z1, z2) :|: z = 1 + (1 + z0906 + z1543 + z2180) + z1 + z2, z1 >= 0, z2180 >= 0, z0906 >= 0, z1543 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(a__diff(mark(z0907), mark(z1544)), z1, z2) :|: z1 >= 0, z0907 >= 0, z = 1 + (1 + z0907 + z1544) + z1 + z2, z2 >= 0, z1544 >= 0
   mark(z) -{ 0 }-> a__if(2, z1, z2) :|: z1 >= 0, z = 1 + 2 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__if(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__if(1 + mark(z0908), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0908) + z1 + z2, z0908 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__diff(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: z >= 0
   mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

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

   a__p(v0) -> null_a__p [0]
   a__leq(v0, v1) -> null_a__leq [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   a__diff(v0, v1) -> null_a__diff [0]
   mark(v0) -> null_mark [0]
   A__P(v0) -> null_A__P [0]
   A__LEQ(v0, v1) -> null_A__LEQ [0]
   A__IF(v0, v1, v2) -> null_A__IF [0]
   MARK(v0) -> null_MARK [0]

And the following fresh constants:    null_a__p, null_a__leq, null_a__if, null_a__diff, null_mark, null_A__P, null_A__LEQ, null_A__IF, null_MARK, const

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

(68)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   A__P(s(z0)) -> c1(MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   A__IF(true, z0, z1) -> c8(MARK(z0)) [1]
   A__IF(false, z0, z1) -> c9(MARK(z1)) [1]
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c21(MARK(z0)) [1]
   a__p(0) -> 0 [0]
   a__p(s(z0)) -> mark(z0) [0]
   a__p(z0) -> p(z0) [0]
   a__leq(0, z0) -> true [0]
   a__leq(s(z0), 0) -> false [0]
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1)) [0]
   a__leq(z0, z1) -> leq(z0, z1) [0]
   a__if(true, z0, z1) -> mark(z0) [0]
   a__if(false, z0, z1) -> mark(z1) [0]
   a__if(z0, z1, z2) -> if(z0, z1, z2) [0]
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))) [0]
   a__diff(z0, z1) -> diff(z0, z1) [0]
   mark(p(z0)) -> a__p(mark(z0)) [0]
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1)) [0]
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2) [0]
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1)) [0]
   mark(0) -> 0 [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(true) -> true [0]
   mark(false) -> false [0]
   a__p(v0) -> null_a__p [0]
   a__leq(v0, v1) -> null_a__leq [0]
   a__if(v0, v1, v2) -> null_a__if [0]
   a__diff(v0, v1) -> null_a__diff [0]
   mark(v0) -> null_mark [0]
   A__P(v0) -> null_A__P [0]
   A__LEQ(v0, v1) -> null_A__LEQ [0]
   A__IF(v0, v1, v2) -> null_A__IF [0]
   MARK(v0) -> null_MARK [0]

The TRS has the following type information:
A__P :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c1:null_A__P
s :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c1 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c1:null_A__P
MARK :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c14:c15:c16:c17:c18:c19:c21:null_MARK
A__LEQ :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c5:c6:null_A__LEQ
c5 :: c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c5:c6:null_A__LEQ
mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c6 :: c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c5:c6:null_A__LEQ
A__IF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c8:c9:null_A__IF
true :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c8 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c8:c9:null_A__IF
false :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c9 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c8:c9:null_A__IF
A__DIFF :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> c11:c12
c11 :: c8:c9:null_A__IF -> c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c11:c12
a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
0 :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c12 :: c8:c9:null_A__IF -> c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c11:c12
c14 :: c1:null_A__P -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c15 :: c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
c16 :: c5:c6:null_A__LEQ -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
c17 :: c8:c9:null_A__IF -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
c18 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
c19 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
c21 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK
a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark -> s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__p :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__leq :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__if :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_a__diff :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_mark :: s:true:false:0:p:diff:leq:if:null_a__p:null_a__leq:null_a__if:null_a__diff:null_mark
null_A__P :: c1:null_A__P
null_A__LEQ :: c5:c6:null_A__LEQ
null_A__IF :: c8:c9:null_A__IF
null_MARK :: c14:c15:c16:c17:c18:c19:c21:null_MARK
const :: c11:c12

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

   true => 2
   false => 1
   0 => 0
   null_a__p => 0
   null_a__leq => 0
   null_a__if => 0
   null_a__diff => 0
   null_mark => 0
   null_A__P => 0
   null_A__LEQ => 0
   null_A__IF => 0
   null_MARK => 0
   const => 0

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

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

   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   A__DIFF(z, z') -{ 1 }-> 1 + A__IF(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   A__IF(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   A__IF(z, z', z'') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__LEQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   A__LEQ(z, z') -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   A__P(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__P(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__P(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__LEQ(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__IF(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__DIFF(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__diff(z, z') -{ 0 }-> a__if(a__leq(mark(z0), mark(z1)), 0, 1 + (1 + (1 + z0) + z1)) :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__diff(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__diff(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__if(z, z', z'') -{ 0 }-> mark(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> mark(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__if(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__leq(z, z') -{ 0 }-> a__leq(mark(z0), mark(z1)) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   a__leq(z, z') -{ 0 }-> 2 :|: z0 >= 0, z = 0, z' = z0
   a__leq(z, z') -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0, z' = 0
   a__leq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__leq(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__p(z) -{ 0 }-> mark(z0) :|: z = 1 + z0, z0 >= 0
   a__p(z) -{ 0 }-> 0 :|: z = 0
   a__p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__p(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   mark(z) -{ 0 }-> a__p(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__leq(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__if(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__diff(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> 2 :|: z = 2
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0

Only complete derivations are relevant for the runtime complexity.

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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(z0), s(z1)) -> c5(A__LEQ(mark(z0), mark(z1)), MARK(z0)) by 
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(0)) -> c5(A__LEQ(mark(x0), 0), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(A__LEQ(mark(x0), true), MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(A__LEQ(mark(x0), false), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(x1)) -> c5(A__LEQ(0, mark(x1)), MARK(0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(true), s(x1)) -> c5(A__LEQ(true, mark(x1)), MARK(true))
   A__LEQ(s(false), s(x1)) -> c5(A__LEQ(false, mark(x1)), MARK(false))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(0)) -> c5(A__LEQ(mark(x0), 0), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(A__LEQ(mark(x0), true), MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(A__LEQ(mark(x0), false), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(x1)) -> c5(A__LEQ(0, mark(x1)), MARK(0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(true), s(x1)) -> c5(A__LEQ(true, mark(x1)), MARK(true))
   A__LEQ(s(false), s(x1)) -> c5(A__LEQ(false, mark(x1)), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(0)) -> c5(A__LEQ(mark(x0), 0), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(A__LEQ(mark(x0), true), MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(A__LEQ(mark(x0), false), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(x1)) -> c5(A__LEQ(0, mark(x1)), MARK(0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(true), s(x1)) -> c5(A__LEQ(true, mark(x1)), MARK(true))
   A__LEQ(s(false), s(x1)) -> c5(A__LEQ(false, mark(x1)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c1_1, c6_2, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(false), s(x1)) -> c5(A__LEQ(false, mark(x1)), MARK(false))
   A__LEQ(s(true), s(x1)) -> c5(A__LEQ(true, mark(x1)), MARK(true))
   A__LEQ(s(0), s(x1)) -> c5(A__LEQ(0, mark(x1)), MARK(0))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(0)) -> c5(A__LEQ(mark(x0), 0), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(A__LEQ(mark(x0), true), MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(A__LEQ(mark(x0), false), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(0)) -> c5(A__LEQ(mark(x0), 0), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(A__LEQ(mark(x0), true), MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(A__LEQ(mark(x0), false), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c1_1, c6_2, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2


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

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__LEQ_2, A__IF_3, A__DIFF_2, MARK_1

Compound Symbols:   c1_1, c6_2, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(z0), s(z1)) -> c6(A__LEQ(mark(z0), mark(z1)), MARK(z1)) by 
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(0)) -> c6(A__LEQ(mark(x0), 0), MARK(0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(x0), s(true)) -> c6(A__LEQ(mark(x0), true), MARK(true))
   A__LEQ(s(x0), s(false)) -> c6(A__LEQ(mark(x0), false), MARK(false))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(A__LEQ(0, mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(A__LEQ(true, mark(x1)), MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(A__LEQ(false, mark(x1)), MARK(x1))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(0)) -> c6(A__LEQ(mark(x0), 0), MARK(0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(x0), s(true)) -> c6(A__LEQ(mark(x0), true), MARK(true))
   A__LEQ(s(x0), s(false)) -> c6(A__LEQ(mark(x0), false), MARK(false))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(A__LEQ(0, mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(A__LEQ(true, mark(x1)), MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(A__LEQ(false, mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(0)) -> c6(A__LEQ(mark(x0), 0), MARK(0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(x0), s(true)) -> c6(A__LEQ(mark(x0), true), MARK(true))
   A__LEQ(s(x0), s(false)) -> c6(A__LEQ(mark(x0), false), MARK(false))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(A__LEQ(0, mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(A__LEQ(true, mark(x1)), MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(A__LEQ(false, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, A__DIFF_2, MARK_1, A__LEQ_2

Compound Symbols:   c1_1, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2


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

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(x0), s(false)) -> c6(A__LEQ(mark(x0), false), MARK(false))
   A__LEQ(s(x0), s(true)) -> c6(A__LEQ(mark(x0), true), MARK(true))
   A__LEQ(s(x0), s(0)) -> c6(A__LEQ(mark(x0), 0), MARK(0))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(A__LEQ(0, mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(A__LEQ(true, mark(x1)), MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(A__LEQ(false, mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(A__LEQ(0, mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(A__LEQ(true, mark(x1)), MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(A__LEQ(false, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, A__DIFF_2, MARK_1, A__LEQ_2

Compound Symbols:   c1_1, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2


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

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, A__DIFF_2, MARK_1, A__LEQ_2

Compound Symbols:   c1_1, c8_1, c9_1, c11_3, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(z0, z1) -> c11(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z0)) by 
   A__DIFF(x0, x1) -> c11(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(0))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(true))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(false))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, x1) -> c11(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(0))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(true))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, x1) -> c11(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(0))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(true))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, A__DIFF_2, MARK_1, A__LEQ_2

Compound Symbols:   c1_1, c8_1, c9_1, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, A__DIFF_2, MARK_1, A__LEQ_2

Compound Symbols:   c1_1, c8_1, c9_1, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(z0, z1) -> c12(A__IF(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1))), A__LEQ(mark(z0), mark(z1)), MARK(z1)) by 
   A__DIFF(x0, x1) -> c12(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(0))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(true))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(false))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, x1) -> c12(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(0))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(true))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(false))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, x1) -> c12(A__IF(leq(mark(x0), mark(x1)), 0, s(diff(p(x0), x1))), A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(0))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(true))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(false))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(p(z0)) -> c14(A__P(mark(z0)), MARK(z0)) by 
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(0)) -> c14(A__P(0), MARK(0))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(p(true)) -> c14(A__P(true), MARK(true))
   MARK(p(false)) -> c14(A__P(false), MARK(false))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(0)) -> c14(A__P(0), MARK(0))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(p(true)) -> c14(A__P(true), MARK(true))
   MARK(p(false)) -> c14(A__P(false), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(0)) -> c14(A__P(0), MARK(0))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(p(true)) -> c14(A__P(true), MARK(true))
   MARK(p(false)) -> c14(A__P(false), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2


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

(93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(p(0)) -> c14(A__P(0), MARK(0))
   MARK(p(false)) -> c14(A__P(false), MARK(false))
   MARK(p(true)) -> c14(A__P(true), MARK(true))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c15_2, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(leq(z0, z1)) -> c15(A__LEQ(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, 0)) -> c15(A__LEQ(mark(x0), 0), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(x0, true)) -> c15(A__LEQ(mark(x0), true), MARK(x0))
   MARK(leq(x0, false)) -> c15(A__LEQ(mark(x0), false), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(0, x1)) -> c15(A__LEQ(0, mark(x1)), MARK(0))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(true, x1)) -> c15(A__LEQ(true, mark(x1)), MARK(true))
   MARK(leq(false, x1)) -> c15(A__LEQ(false, mark(x1)), MARK(false))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, 0)) -> c15(A__LEQ(mark(x0), 0), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(x0, true)) -> c15(A__LEQ(mark(x0), true), MARK(x0))
   MARK(leq(x0, false)) -> c15(A__LEQ(mark(x0), false), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(0, x1)) -> c15(A__LEQ(0, mark(x1)), MARK(0))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(true, x1)) -> c15(A__LEQ(true, mark(x1)), MARK(true))
   MARK(leq(false, x1)) -> c15(A__LEQ(false, mark(x1)), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, 0)) -> c15(A__LEQ(mark(x0), 0), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(x0, true)) -> c15(A__LEQ(mark(x0), true), MARK(x0))
   MARK(leq(x0, false)) -> c15(A__LEQ(mark(x0), false), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(0, x1)) -> c15(A__LEQ(0, mark(x1)), MARK(0))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(true, x1)) -> c15(A__LEQ(true, mark(x1)), MARK(true))
   MARK(leq(false, x1)) -> c15(A__LEQ(false, mark(x1)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2


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

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(leq(0, x1)) -> c15(A__LEQ(0, mark(x1)), MARK(0))
   MARK(leq(true, x1)) -> c15(A__LEQ(true, mark(x1)), MARK(true))
   MARK(leq(false, x1)) -> c15(A__LEQ(false, mark(x1)), MARK(false))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, 0)) -> c15(A__LEQ(mark(x0), 0), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(x0, true)) -> c15(A__LEQ(mark(x0), true), MARK(x0))
   MARK(leq(x0, false)) -> c15(A__LEQ(mark(x0), false), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, 0)) -> c15(A__LEQ(mark(x0), 0), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(x0, true)) -> c15(A__LEQ(mark(x0), true), MARK(x0))
   MARK(leq(x0, false)) -> c15(A__LEQ(mark(x0), false), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c16_2, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(leq(z0, z1)) -> c16(A__LEQ(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, 0)) -> c16(A__LEQ(mark(x0), 0), MARK(0))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, true)) -> c16(A__LEQ(mark(x0), true), MARK(true))
   MARK(leq(x0, false)) -> c16(A__LEQ(mark(x0), false), MARK(false))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(A__LEQ(0, mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(true, x1)) -> c16(A__LEQ(true, mark(x1)), MARK(x1))
   MARK(leq(false, x1)) -> c16(A__LEQ(false, mark(x1)), MARK(x1))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, 0)) -> c16(A__LEQ(mark(x0), 0), MARK(0))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, true)) -> c16(A__LEQ(mark(x0), true), MARK(true))
   MARK(leq(x0, false)) -> c16(A__LEQ(mark(x0), false), MARK(false))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(A__LEQ(0, mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(true, x1)) -> c16(A__LEQ(true, mark(x1)), MARK(x1))
   MARK(leq(false, x1)) -> c16(A__LEQ(false, mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, 0)) -> c16(A__LEQ(mark(x0), 0), MARK(0))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, true)) -> c16(A__LEQ(mark(x0), true), MARK(true))
   MARK(leq(x0, false)) -> c16(A__LEQ(mark(x0), false), MARK(false))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(A__LEQ(0, mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(true, x1)) -> c16(A__LEQ(true, mark(x1)), MARK(x1))
   MARK(leq(false, x1)) -> c16(A__LEQ(false, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2


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

(103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(leq(x0, 0)) -> c16(A__LEQ(mark(x0), 0), MARK(0))
   MARK(leq(x0, false)) -> c16(A__LEQ(mark(x0), false), MARK(false))
   MARK(leq(x0, true)) -> c16(A__LEQ(mark(x0), true), MARK(true))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(A__LEQ(0, mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(true, x1)) -> c16(A__LEQ(true, mark(x1)), MARK(x1))
   MARK(leq(false, x1)) -> c16(A__LEQ(false, mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(A__LEQ(0, mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(true, x1)) -> c16(A__LEQ(true, mark(x1)), MARK(x1))
   MARK(leq(false, x1)) -> c16(A__LEQ(false, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c17_2, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(if(z0, z1, z2)) -> c17(A__IF(mark(z0), z1, z2), MARK(z0)) by 
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(0, x1, x2)) -> c17(A__IF(0, x1, x2), MARK(0))
   MARK(if(s(z0), x1, x2)) -> c17(A__IF(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2), MARK(true))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2), MARK(false))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(0, x1, x2)) -> c17(A__IF(0, x1, x2), MARK(0))
   MARK(if(s(z0), x1, x2)) -> c17(A__IF(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2), MARK(true))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(0, x1, x2)) -> c17(A__IF(0, x1, x2), MARK(0))
   MARK(if(s(z0), x1, x2)) -> c17(A__IF(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2), MARK(true))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2


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

(109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(if(0, x1, x2)) -> c17(A__IF(0, x1, x2), MARK(0))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(A__IF(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2), MARK(true))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(A__IF(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2), MARK(true))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2


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

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(p(z0))) -> c5(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0)) by 
   A__LEQ(s(x0), s(p(x1))) -> c5(A__LEQ(mark(x0), p(mark(x1))), MARK(x0))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(p(x1))) -> c5(A__LEQ(0, a__p(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(p(x1))) -> c5(A__LEQ(true, a__p(mark(x1))), MARK(true))
   A__LEQ(s(false), s(p(x1))) -> c5(A__LEQ(false, a__p(mark(x1))), MARK(false))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(x1))) -> c5(A__LEQ(mark(x0), p(mark(x1))), MARK(x0))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(p(x1))) -> c5(A__LEQ(0, a__p(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(p(x1))) -> c5(A__LEQ(true, a__p(mark(x1))), MARK(true))
   A__LEQ(s(false), s(p(x1))) -> c5(A__LEQ(false, a__p(mark(x1))), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(x1))) -> c5(A__LEQ(mark(x0), p(mark(x1))), MARK(x0))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(p(x1))) -> c5(A__LEQ(0, a__p(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(p(x1))) -> c5(A__LEQ(true, a__p(mark(x1))), MARK(true))
   A__LEQ(s(false), s(p(x1))) -> c5(A__LEQ(false, a__p(mark(x1))), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(true), s(p(x1))) -> c5(A__LEQ(true, a__p(mark(x1))), MARK(true))
   A__LEQ(s(false), s(p(x1))) -> c5(A__LEQ(false, a__p(mark(x1))), MARK(false))
   A__LEQ(s(0), s(p(x1))) -> c5(A__LEQ(0, a__p(mark(x1))), MARK(0))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(x1))) -> c5(A__LEQ(mark(x0), p(mark(x1))), MARK(x0))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(x1))) -> c5(A__LEQ(mark(x0), p(mark(x1))), MARK(x0))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(leq(z0, z1))) -> c5(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0)) by 
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c5(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c5(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(leq(x1, x2))) -> c5(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(false))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c5(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c5(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(leq(x1, x2))) -> c5(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c5(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c5(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(leq(x1, x2))) -> c5(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(true), s(leq(x1, x2))) -> c5(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(0), s(leq(x1, x2))) -> c5(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(false), s(leq(x1, x2))) -> c5(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(false))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(if(z0, z1, z2))) -> c5(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0)) by 
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c5(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(0))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c5(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(true))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c5(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(false))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c5(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(0))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c5(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(true))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c5(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c5(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(0))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c5(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(true))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c5(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c5(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(0))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c5(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(true))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c5(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(false))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(diff(z0, z1))) -> c5(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0)) by 
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c5(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c5(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(diff(x1, x2))) -> c5(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(false))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c5(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c5(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(diff(x1, x2))) -> c5(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c5(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(0))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c5(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(false), s(diff(x1, x2))) -> c5(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(false), s(diff(x1, x2))) -> c5(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(false))
   A__LEQ(s(true), s(diff(x1, x2))) -> c5(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(true))
   A__LEQ(s(0), s(diff(x1, x2))) -> c5(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(0))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(s(z0))) -> c5(A__LEQ(mark(x0), s(mark(z0))), MARK(x0)) by 
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(s(x1))) -> c5(A__LEQ(0, s(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(s(x1))) -> c5(A__LEQ(true, s(mark(x1))), MARK(true))
   A__LEQ(s(false), s(s(x1))) -> c5(A__LEQ(false, s(mark(x1))), MARK(false))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(s(x1))) -> c5(A__LEQ(0, s(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(s(x1))) -> c5(A__LEQ(true, s(mark(x1))), MARK(true))
   A__LEQ(s(false), s(s(x1))) -> c5(A__LEQ(false, s(mark(x1))), MARK(false))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
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   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(0), s(s(x1))) -> c5(A__LEQ(0, s(mark(x1))), MARK(0))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(true), s(s(x1))) -> c5(A__LEQ(true, s(mark(x1))), MARK(true))
   A__LEQ(s(false), s(s(x1))) -> c5(A__LEQ(false, s(mark(x1))), MARK(false))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(0), s(s(x1))) -> c5(A__LEQ(0, s(mark(x1))), MARK(0))
   A__LEQ(s(true), s(s(x1))) -> c5(A__LEQ(true, s(mark(x1))), MARK(true))
   A__LEQ(s(false), s(s(x1))) -> c5(A__LEQ(false, s(mark(x1))), MARK(false))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
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   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
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   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
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   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(p(z0)), s(x1)) -> c5(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0))) by 
   A__LEQ(s(p(x0)), s(p(z0))) -> c5(A__LEQ(a__p(mark(x0)), a__p(mark(z0))), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(leq(z0, z1))) -> c5(A__LEQ(a__p(mark(x0)), a__leq(mark(z0), mark(z1))), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(if(z0, z1, z2))) -> c5(A__LEQ(a__p(mark(x0)), a__if(mark(z0), z1, z2)), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(diff(z0, z1))) -> c5(A__LEQ(a__p(mark(x0)), a__diff(mark(z0), mark(z1))), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(0)) -> c5(A__LEQ(a__p(mark(x0)), 0), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(s(z0))) -> c5(A__LEQ(a__p(mark(x0)), s(mark(z0))), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(A__LEQ(a__p(mark(x0)), true), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(A__LEQ(a__p(mark(x0)), false), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(A__LEQ(p(mark(x0)), mark(x1)), MARK(p(x0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)), MARK(p(0)))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)), MARK(p(true)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)), MARK(p(false)))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(x0)), s(0)) -> c5(A__LEQ(a__p(mark(x0)), 0), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(A__LEQ(a__p(mark(x0)), true), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(A__LEQ(a__p(mark(x0)), false), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(A__LEQ(p(mark(x0)), mark(x1)), MARK(p(x0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)), MARK(p(0)))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)), MARK(p(true)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)), MARK(p(false)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
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   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
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   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
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   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(x0)), s(0)) -> c5(A__LEQ(a__p(mark(x0)), 0), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(A__LEQ(a__p(mark(x0)), true), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(A__LEQ(a__p(mark(x0)), false), MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(A__LEQ(p(mark(x0)), mark(x1)), MARK(p(x0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)), MARK(p(0)))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)), MARK(p(true)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)), MARK(p(false)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(leq(z0, z1)), s(x1)) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1))) by 
   A__LEQ(s(leq(x0, x1)), s(p(z0))) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), a__p(mark(z0))), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(leq(z0, z1))) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), a__leq(mark(z0), mark(z1))), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(if(z0, z1, z2))) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(diff(z0, z1))) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), a__diff(mark(z0), mark(z1))), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(s(z0))) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), s(mark(z0))), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
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   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
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   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c5(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2))) by 
   A__LEQ(s(if(x0, x1, x2)), s(p(z0))) -> c5(A__LEQ(a__if(mark(x0), x1, x2), a__p(mark(z0))), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(leq(z0, z1))) -> c5(A__LEQ(a__if(mark(x0), x1, x2), a__leq(mark(z0), mark(z1))), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(if(z0, z1, z2))) -> c5(A__LEQ(a__if(mark(x0), x1, x2), a__if(mark(z0), z1, z2)), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(diff(z0, z1))) -> c5(A__LEQ(a__if(mark(x0), x1, x2), a__diff(mark(z0), mark(z1))), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(s(z0))) -> c5(A__LEQ(a__if(mark(x0), x1, x2), s(mark(z0))), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(if(x0, z1, z2)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(if(0, x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
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   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(diff(z0, z1)), s(x1)) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1))) by 
   A__LEQ(s(diff(x0, x1)), s(p(z0))) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), a__p(mark(z0))), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(leq(z0, z1))) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), a__leq(mark(z0), mark(z1))), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(if(z0, z1, z2))) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(diff(z0, z1))) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), a__diff(mark(z0), mark(z1))), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(s(z0))) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), s(mark(z0))), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_2, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(s(z0)), s(x1)) -> c5(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0))) by 
   A__LEQ(s(s(x0)), s(p(z0))) -> c5(A__LEQ(s(mark(x0)), a__p(mark(z0))), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(leq(z0, z1))) -> c5(A__LEQ(s(mark(x0)), a__leq(mark(z0), mark(z1))), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(if(z0, z1, z2))) -> c5(A__LEQ(s(mark(x0)), a__if(mark(z0), z1, z2)), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(diff(z0, z1))) -> c5(A__LEQ(s(mark(x0)), a__diff(mark(z0), mark(z1))), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(A__LEQ(s(mark(x0)), 0), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(s(z0))) -> c5(A__LEQ(s(mark(x0)), s(mark(z0))), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(A__LEQ(s(mark(x0)), true), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(A__LEQ(s(mark(x0)), false), MARK(s(x0)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(x0)), s(0)) -> c5(A__LEQ(s(mark(x0)), 0), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(A__LEQ(s(mark(x0)), true), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(A__LEQ(s(mark(x0)), false), MARK(s(x0)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
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   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(x0)), s(0)) -> c5(A__LEQ(s(mark(x0)), 0), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(A__LEQ(s(mark(x0)), true), MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(A__LEQ(s(mark(x0)), false), MARK(s(x0)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
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   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(p(z0))) -> c6(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0))) by 
   A__LEQ(s(x0), s(p(x1))) -> c6(A__LEQ(mark(x0), p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)), MARK(p(0)))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)), MARK(p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)), MARK(p(false)))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(0), s(p(x1))) -> c6(A__LEQ(0, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(A__LEQ(true, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(A__LEQ(false, a__p(mark(x1))), MARK(p(x1)))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
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   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(x1))) -> c6(A__LEQ(mark(x0), p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)), MARK(p(0)))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)), MARK(p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)), MARK(p(false)))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(0), s(p(x1))) -> c6(A__LEQ(0, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(A__LEQ(true, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(A__LEQ(false, a__p(mark(x1))), MARK(p(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(x1))) -> c6(A__LEQ(mark(x0), p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)), MARK(p(0)))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)), MARK(p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)), MARK(p(false)))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(0), s(p(x1))) -> c6(A__LEQ(0, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(A__LEQ(true, a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(A__LEQ(false, a__p(mark(x1))), MARK(p(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
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   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
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   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(leq(z0, z1))) -> c6(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1))) by 
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
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   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(A__LEQ(mark(x0), leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(A__LEQ(0, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(A__LEQ(true, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(A__LEQ(false, a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(if(z0, z1, z2))) -> c6(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2))) by 
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(A__LEQ(mark(x0), if(mark(x1), z1, z2)), MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(if(0, x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(A__LEQ(0, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(A__LEQ(true, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(A__LEQ(false, a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
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   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
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   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(diff(z0, z1))) -> c6(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1))) by 
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
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   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
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   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(A__LEQ(0, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(A__LEQ(true, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(A__LEQ(false, a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(x0), s(s(z0))) -> c6(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0))) by 
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(A__LEQ(0, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(A__LEQ(true, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(A__LEQ(false, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
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   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(A__LEQ(0, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(A__LEQ(true, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(A__LEQ(false, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
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   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
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   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
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   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
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   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
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   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(A__LEQ(0, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(A__LEQ(true, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(A__LEQ(false, s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
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   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
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   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(p(z0)), s(x1)) -> c6(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1)) by 
   A__LEQ(s(p(x0)), s(p(z0))) -> c6(A__LEQ(a__p(mark(x0)), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(p(x0)), s(leq(z0, z1))) -> c6(A__LEQ(a__p(mark(x0)), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(p(x0)), s(if(z0, z1, z2))) -> c6(A__LEQ(a__p(mark(x0)), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(p(x0)), s(diff(z0, z1))) -> c6(A__LEQ(a__p(mark(x0)), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(p(x0)), s(0)) -> c6(A__LEQ(a__p(mark(x0)), 0), MARK(0))
   A__LEQ(s(p(x0)), s(s(z0))) -> c6(A__LEQ(a__p(mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(p(x0)), s(true)) -> c6(A__LEQ(a__p(mark(x0)), true), MARK(true))
   A__LEQ(s(p(x0)), s(false)) -> c6(A__LEQ(a__p(mark(x0)), false), MARK(false))
   A__LEQ(s(p(x0)), s(x1)) -> c6(A__LEQ(p(mark(x0)), mark(x1)), MARK(x1))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(x0)), s(0)) -> c6(A__LEQ(a__p(mark(x0)), 0), MARK(0))
   A__LEQ(s(p(x0)), s(true)) -> c6(A__LEQ(a__p(mark(x0)), true), MARK(true))
   A__LEQ(s(p(x0)), s(false)) -> c6(A__LEQ(a__p(mark(x0)), false), MARK(false))
   A__LEQ(s(p(x0)), s(x1)) -> c6(A__LEQ(p(mark(x0)), mark(x1)), MARK(x1))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
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   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
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   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(x0)), s(0)) -> c6(A__LEQ(a__p(mark(x0)), 0), MARK(0))
   A__LEQ(s(p(x0)), s(true)) -> c6(A__LEQ(a__p(mark(x0)), true), MARK(true))
   A__LEQ(s(p(x0)), s(false)) -> c6(A__LEQ(a__p(mark(x0)), false), MARK(false))
   A__LEQ(s(p(x0)), s(x1)) -> c6(A__LEQ(p(mark(x0)), mark(x1)), MARK(x1))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(183) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(p(x0)), s(false)) -> c6(A__LEQ(a__p(mark(x0)), false), MARK(false))
   A__LEQ(s(p(x0)), s(0)) -> c6(A__LEQ(a__p(mark(x0)), 0), MARK(0))
   A__LEQ(s(p(x0)), s(true)) -> c6(A__LEQ(a__p(mark(x0)), true), MARK(true))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
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   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
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   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(x0)), s(x1)) -> c6(A__LEQ(p(mark(x0)), mark(x1)), MARK(x1))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(x0)), s(x1)) -> c6(A__LEQ(p(mark(x0)), mark(x1)), MARK(x1))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(leq(z0, z1)), s(x1)) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by 
   A__LEQ(s(leq(x0, x1)), s(p(z0))) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(leq(x0, x1)), s(leq(z0, z1))) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(leq(x0, x1)), s(if(z0, z1, z2))) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(leq(x0, x1)), s(diff(z0, z1))) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(leq(x0, x1)), s(s(z0))) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
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   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
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   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(leq(x0, x1)), s(false)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c6(A__LEQ(a__leq(mark(x0), mark(x1)), 0), MARK(0))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
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   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
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   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
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   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
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   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
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   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
   A__LEQ(s(x0), s(p(false))) -> c6(A__LEQ(mark(x0), a__p(false)))
   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(false), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(A__LEQ(leq(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
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   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
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   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
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   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
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   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
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   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
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   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
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   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
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   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(true), s(p(x1))) -> c6(MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(leq(x1, p(z0))))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(if(z0, z1, z2)), s(x1)) -> c6(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1)) by 
   A__LEQ(s(if(x0, x1, x2)), s(p(z0))) -> c6(A__LEQ(a__if(mark(x0), x1, x2), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(if(x0, x1, x2)), s(leq(z0, z1))) -> c6(A__LEQ(a__if(mark(x0), x1, x2), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(x0, x1, x2)), s(if(z0, z1, z2))) -> c6(A__LEQ(a__if(mark(x0), x1, x2), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(if(x0, x1, x2)), s(diff(z0, z1))) -> c6(A__LEQ(a__if(mark(x0), x1, x2), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(0))
   A__LEQ(s(if(x0, x1, x2)), s(s(z0))) -> c6(A__LEQ(a__if(mark(x0), x1, x2), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(true))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(false))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(x3))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
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   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
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   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(0))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(true))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(false))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(x3))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
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   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(0))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(true))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(false))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(x3))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(195) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), true), MARK(true))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), 0), MARK(0))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c6(A__LEQ(a__if(mark(x0), x1, x2), false), MARK(false))

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(x3))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
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   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
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   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(A__LEQ(if(mark(x0), z1, z2), mark(x3)), MARK(x3))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
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   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
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   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(199) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(diff(z0, z1)), s(x1)) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by 
   A__LEQ(s(diff(x0, x1)), s(p(z0))) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(diff(x0, x1)), s(leq(z0, z1))) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(diff(x0, x1)), s(if(z0, z1, z2))) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(x0, x1)), s(diff(z0, z1))) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(diff(x0, x1)), s(s(z0))) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(true))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(201) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(diff(x0, x1)), s(0)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), 0), MARK(0))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), false), MARK(false))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c6(A__LEQ(a__diff(mark(x0), mark(x1)), true), MARK(true))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
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   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(diff(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
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   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
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   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
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   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
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   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_2, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2


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

(205) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__LEQ(s(s(z0)), s(x1)) -> c6(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1)) by 
   A__LEQ(s(s(x0)), s(p(z0))) -> c6(A__LEQ(s(mark(x0)), a__p(mark(z0))), MARK(p(z0)))
   A__LEQ(s(s(x0)), s(leq(z0, z1))) -> c6(A__LEQ(s(mark(x0)), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   A__LEQ(s(s(x0)), s(if(z0, z1, z2))) -> c6(A__LEQ(s(mark(x0)), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   A__LEQ(s(s(x0)), s(diff(z0, z1))) -> c6(A__LEQ(s(mark(x0)), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(x0)), s(0)) -> c6(A__LEQ(s(mark(x0)), 0), MARK(0))
   A__LEQ(s(s(x0)), s(s(z0))) -> c6(A__LEQ(s(mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__LEQ(s(s(x0)), s(true)) -> c6(A__LEQ(s(mark(x0)), true), MARK(true))
   A__LEQ(s(s(x0)), s(false)) -> c6(A__LEQ(s(mark(x0)), false), MARK(false))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
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   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(x0)), s(0)) -> c6(A__LEQ(s(mark(x0)), 0), MARK(0))
   A__LEQ(s(s(x0)), s(true)) -> c6(A__LEQ(s(mark(x0)), true), MARK(true))
   A__LEQ(s(s(x0)), s(false)) -> c6(A__LEQ(s(mark(x0)), false), MARK(false))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(x0)), s(0)) -> c6(A__LEQ(s(mark(x0)), 0), MARK(0))
   A__LEQ(s(s(x0)), s(true)) -> c6(A__LEQ(s(mark(x0)), true), MARK(true))
   A__LEQ(s(s(x0)), s(false)) -> c6(A__LEQ(s(mark(x0)), false), MARK(false))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2


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

(207) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   A__LEQ(s(s(x0)), s(true)) -> c6(A__LEQ(s(mark(x0)), true), MARK(true))
   A__LEQ(s(s(x0)), s(false)) -> c6(A__LEQ(s(mark(x0)), false), MARK(false))
   A__LEQ(s(s(x0)), s(0)) -> c6(A__LEQ(s(mark(x0)), 0), MARK(0))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
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   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
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   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2


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

(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, p(z0)) -> c11(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(x0)) by 
   A__DIFF(x0, p(x1)) -> c11(A__IF(leq(mark(x0), a__p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))), MARK(0))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))), MARK(true))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))), MARK(false))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
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   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(leq(mark(x0), a__p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))), MARK(0))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))), MARK(true))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))), MARK(false))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
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   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(leq(mark(x0), a__p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))), MARK(0))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))), MARK(true))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))), MARK(false))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
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   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
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   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
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   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
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   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
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   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
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   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, leq(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(x0)) by 
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(leq(mark(x0), a__leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))), MARK(0))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))), MARK(true))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))), MARK(false))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(leq(mark(x0), a__leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))), MARK(0))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))), MARK(true))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))), MARK(false))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(leq(mark(x0), a__leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))), MARK(0))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))), MARK(true))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))), MARK(false))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
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   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
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   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
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   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
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   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, if(z0, z1, z2)) -> c11(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(x0)) by 
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__IF(leq(mark(x0), a__if(mark(x1), x2, x3)), 0, s(diff(p(x0), if(x1, x2, x3)))), A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))), MARK(0))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))), MARK(true))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))), MARK(false))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
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   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
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   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__IF(leq(mark(x0), a__if(mark(x1), x2, x3)), 0, s(diff(p(x0), if(x1, x2, x3)))), A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))), MARK(0))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))), MARK(true))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))), MARK(false))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__IF(leq(mark(x0), a__if(mark(x1), x2, x3)), 0, s(diff(p(x0), if(x1, x2, x3)))), A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))), MARK(0))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))), MARK(true))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))), MARK(false))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, diff(z0, z1)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(x0)) by 
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(leq(mark(x0), a__diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))), MARK(0))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))), MARK(true))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))), MARK(false))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
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   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
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   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
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   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(if(p(z0), x2, x3)))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
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   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
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   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
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   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
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   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(leq(mark(x0), a__diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))), MARK(0))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))), MARK(true))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))), MARK(false))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
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   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
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   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(leq(mark(x0), a__diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))), MARK(0))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))), MARK(true))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))), MARK(false))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
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   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
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   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
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   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
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   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
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   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
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   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
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   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, 0) -> c11(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0)) by 
   A__DIFF(x0, 0) -> c11(A__IF(leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)), MARK(0))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)), MARK(true))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)), MARK(false))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(x0, 0) -> c11(A__IF(leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)), MARK(0))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)), MARK(true))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)), MARK(false))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
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   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
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   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(x0, 0) -> c11(A__IF(leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)), MARK(0))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)), MARK(true))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)), MARK(false))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
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   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(false), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
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   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
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   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(229) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, s(z0)) -> c11(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(x0)) by 
   A__DIFF(x0, s(x1)) -> c11(A__IF(leq(mark(x0), s(mark(x1))), 0, s(diff(p(x0), s(x1)))), A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))), MARK(0))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))), MARK(true))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))), MARK(false))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(x1)) -> c11(A__IF(leq(mark(x0), s(mark(x1))), 0, s(diff(p(x0), s(x1)))), A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))), MARK(0))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))), MARK(true))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))), MARK(false))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
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   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
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   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
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   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(x1)) -> c11(A__IF(leq(mark(x0), s(mark(x1))), 0, s(diff(p(x0), s(x1)))), A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))), MARK(0))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))), MARK(true))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))), MARK(false))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
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   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
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   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, true) -> c11(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0)) by 
   A__DIFF(x0, true) -> c11(A__IF(leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)), MARK(0))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)), MARK(true))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)), MARK(false))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(x0, true) -> c11(A__IF(leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)), MARK(0))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)), MARK(true))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)), MARK(false))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
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   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
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   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(x0, true) -> c11(A__IF(leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)), MARK(0))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)), MARK(true))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)), MARK(false))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
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   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
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   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
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   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
   A__LEQ(s(p(z0)), s(p(x1))) -> c6(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c6(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(p(x1)))
   A__LEQ(s(x0), s(p(x1))) -> c6(MARK(p(x1)))
   A__LEQ(s(x0), s(p(0))) -> c6(A__LEQ(mark(x0), a__p(0)))
   A__LEQ(s(x0), s(p(true))) -> c6(A__LEQ(mark(x0), a__p(true)))
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   A__LEQ(s(0), s(p(x1))) -> c6(MARK(p(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(leq(x1, 0)))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(leq(x1, s(z0))))
   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
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   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(leq(s(z0), x2)))
   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
   A__LEQ(s(x0), s(leq(false, x2))) -> c6(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(leq(false, x2)))
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   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
   A__LEQ(s(true), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(237) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(x0, false) -> c11(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0)) by 
   A__DIFF(x0, false) -> c11(A__IF(leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)), MARK(0))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)), MARK(true))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)), MARK(false))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
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   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
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   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
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   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(x0, false) -> c11(A__IF(leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)), MARK(0))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)), MARK(true))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)), MARK(false))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
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   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
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   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
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   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
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   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
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   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
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   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
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   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
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   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(leq(x1, diff(z0, z1))))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(x0, false) -> c11(A__IF(leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)), MARK(0))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)), MARK(true))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)), MARK(false))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
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   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
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   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(241) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(p(z0), x1) -> c11(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(p(z0))) by 
   A__DIFF(p(x0), x1) -> c11(A__IF(leq(a__p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(x0), p(z0)) -> c11(A__IF(a__leq(a__p(mark(x0)), a__p(mark(z0))), 0, s(diff(p(p(x0)), p(z0)))), A__LEQ(mark(p(x0)), mark(p(z0))), MARK(p(x0)))
   A__DIFF(p(x0), leq(z0, z1)) -> c11(A__IF(a__leq(a__p(mark(x0)), a__leq(mark(z0), mark(z1))), 0, s(diff(p(p(x0)), leq(z0, z1)))), A__LEQ(mark(p(x0)), mark(leq(z0, z1))), MARK(p(x0)))
   A__DIFF(p(x0), if(z0, z1, z2)) -> c11(A__IF(a__leq(a__p(mark(x0)), a__if(mark(z0), z1, z2)), 0, s(diff(p(p(x0)), if(z0, z1, z2)))), A__LEQ(mark(p(x0)), mark(if(z0, z1, z2))), MARK(p(x0)))
   A__DIFF(p(x0), diff(z0, z1)) -> c11(A__IF(a__leq(a__p(mark(x0)), a__diff(mark(z0), mark(z1))), 0, s(diff(p(p(x0)), diff(z0, z1)))), A__LEQ(mark(p(x0)), mark(diff(z0, z1))), MARK(p(x0)))
   A__DIFF(p(x0), 0) -> c11(A__IF(a__leq(a__p(mark(x0)), 0), 0, s(diff(p(p(x0)), 0))), A__LEQ(mark(p(x0)), mark(0)), MARK(p(x0)))
   A__DIFF(p(x0), s(z0)) -> c11(A__IF(a__leq(a__p(mark(x0)), s(mark(z0))), 0, s(diff(p(p(x0)), s(z0)))), A__LEQ(mark(p(x0)), mark(s(z0))), MARK(p(x0)))
   A__DIFF(p(x0), true) -> c11(A__IF(a__leq(a__p(mark(x0)), true), 0, s(diff(p(p(x0)), true))), A__LEQ(mark(p(x0)), mark(true)), MARK(p(x0)))
   A__DIFF(p(x0), false) -> c11(A__IF(a__leq(a__p(mark(x0)), false), 0, s(diff(p(p(x0)), false))), A__LEQ(mark(p(x0)), mark(false)), MARK(p(x0)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)), MARK(p(0)))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)), MARK(p(true)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)), MARK(p(false)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))

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

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
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   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
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   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(leq(a__p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)), MARK(p(0)))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)), MARK(p(true)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)), MARK(p(false)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(leq(a__p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)), MARK(p(0)))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)), MARK(p(true)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)), MARK(p(false)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
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   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c6(MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(if(if(z0, z1, z2), x2, x3)))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(if(diff(z0, z1), x2, x3)))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(if(s(z0), x2, x3)))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
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   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
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   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
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   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
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   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
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   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
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   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
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   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
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   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
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   A__LEQ(s(x0), s(leq(x1, true))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(leq(x1, true)))
   A__LEQ(s(x0), s(leq(x1, false))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(leq(x1, false)))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(leq(p(z0), x2)))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
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   A__LEQ(s(x0), s(leq(0, x2))) -> c6(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(leq(0, x2)))
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   A__LEQ(s(x0), s(leq(true, x2))) -> c6(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(leq(true, x2)))
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   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
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   A__LEQ(s(x0), s(if(true, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(if(true, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
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   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
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   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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(245) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(leq(z0, z1), x1) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(leq(z0, z1))) by 
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(leq(a__leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), p(z0)) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), a__p(mark(z0))), 0, s(diff(p(leq(x0, x1)), p(z0)))), A__LEQ(mark(leq(x0, x1)), mark(p(z0))), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), leq(z0, z1)) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), a__leq(mark(z0), mark(z1))), 0, s(diff(p(leq(x0, x1)), leq(z0, z1)))), A__LEQ(mark(leq(x0, x1)), mark(leq(z0, z1))), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), if(z0, z1, z2)) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), a__if(mark(z0), z1, z2)), 0, s(diff(p(leq(x0, x1)), if(z0, z1, z2)))), A__LEQ(mark(leq(x0, x1)), mark(if(z0, z1, z2))), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), diff(z0, z1)) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), a__diff(mark(z0), mark(z1))), 0, s(diff(p(leq(x0, x1)), diff(z0, z1)))), A__LEQ(mark(leq(x0, x1)), mark(diff(z0, z1))), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), 0) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), 0), 0, s(diff(p(leq(x0, x1)), 0))), A__LEQ(mark(leq(x0, x1)), mark(0)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), s(z0)) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), s(mark(z0))), 0, s(diff(p(leq(x0, x1)), s(z0)))), A__LEQ(mark(leq(x0, x1)), mark(s(z0))), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), true) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), true), 0, s(diff(p(leq(x0, x1)), true))), A__LEQ(mark(leq(x0, x1)), mark(true)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), false) -> c11(A__IF(a__leq(a__leq(mark(x0), mark(x1)), false), 0, s(diff(p(leq(x0, x1)), false))), A__LEQ(mark(leq(x0, x1)), mark(false)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))

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

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c5(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(diff(true, x1)))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c5(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(diff(false, x1)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(0)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(true)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, x1)), s(false)) -> c5(MARK(diff(x0, x1)))
   A__LEQ(s(s(p(z0))), s(x1)) -> c5(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(s(p(z0))))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
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   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(leq(a__leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
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   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
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   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
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   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(leq(a__leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
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   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
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   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
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   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
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   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
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   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
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   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
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   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
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   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
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   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
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   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
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   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c5(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(z0)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c5(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(p(p(z0))))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c5(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__LEQ(s(p(s(z0))), s(x1)) -> c5(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(p(s(z0))))
   A__LEQ(s(p(x0)), s(0)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(true)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(false)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(x0)), s(x1)) -> c5(MARK(p(x0)))
   A__LEQ(s(p(0)), s(x1)) -> c5(A__LEQ(a__p(0), mark(x1)))
   A__LEQ(s(p(true)), s(x1)) -> c5(A__LEQ(a__p(true), mark(x1)))
   A__LEQ(s(p(false)), s(x1)) -> c5(A__LEQ(a__p(false), mark(x1)))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(leq(x0, 0)))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(leq(x0, true)))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c5(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(leq(x0, false)))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c5(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(leq(0, x1)))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c5(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(leq(true, x1)))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c5(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(leq(false, x1)))
   A__LEQ(s(leq(x0, x1)), s(0)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(true)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(false)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c5(MARK(leq(x0, x1)))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c5(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(if(true, x1, x2)))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(if(false, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(0)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(true)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, x1, x2)), s(false)) -> c5(MARK(if(x0, x1, x2)))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c5(MARK(if(x0, z1, z2)))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c5(A__LEQ(a__if(0, x1, x2), mark(x3)))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c5(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(diff(x0, x1)))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(diff(x0, p(z0))))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, leq(z0, z1))))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(diff(x0, if(z0, z1, z2))))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(diff(x0, diff(z0, z1))))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(diff(x0, 0)))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(diff(x0, s(z0))))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(diff(x0, true)))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c5(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(diff(x0, false)))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(diff(p(z0), x1)))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(leq(z0, z1), x1)))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(diff(if(z0, z1, z2), x1)))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c5(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(diff(diff(z0, z1), x1)))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c5(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(diff(0, x1)))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c5(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(diff(s(z0), x1)))
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   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(s(leq(z0, z1))))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c5(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c5(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(s(diff(z0, z1))))
   A__LEQ(s(s(0)), s(x1)) -> c5(A__LEQ(s(0), mark(x1)), MARK(s(0)))
   A__LEQ(s(s(s(z0))), s(x1)) -> c5(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(s(s(z0))))
   A__LEQ(s(s(true)), s(x1)) -> c5(A__LEQ(s(true), mark(x1)), MARK(s(true)))
   A__LEQ(s(s(false)), s(x1)) -> c5(A__LEQ(s(false), mark(x1)), MARK(s(false)))
   A__LEQ(s(s(x0)), s(x1)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(0)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(true)) -> c5(MARK(s(x0)))
   A__LEQ(s(s(x0)), s(false)) -> c5(MARK(s(x0)))
   A__LEQ(s(x0), s(p(p(z0)))) -> c6(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(p(p(z0))))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(p(leq(z0, z1))))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(p(if(z0, z1, z2))))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(p(diff(z0, z1))))
   A__LEQ(s(x0), s(p(s(z0)))) -> c6(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(p(s(z0))))
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   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

(249) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__DIFF(if(z0, z1, z2), x1) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(if(z0, z1, z2))) by 
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__IF(leq(a__if(mark(x0), x1, x2), mark(x3)), 0, s(diff(p(if(x0, x1, x2)), x3))), A__LEQ(mark(if(x0, x1, x2)), mark(x3)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), p(z0)) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), a__p(mark(z0))), 0, s(diff(p(if(x0, x1, x2)), p(z0)))), A__LEQ(mark(if(x0, x1, x2)), mark(p(z0))), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), leq(z0, z1)) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), a__leq(mark(z0), mark(z1))), 0, s(diff(p(if(x0, x1, x2)), leq(z0, z1)))), A__LEQ(mark(if(x0, x1, x2)), mark(leq(z0, z1))), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), if(z0, z1, z2)) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), a__if(mark(z0), z1, z2)), 0, s(diff(p(if(x0, x1, x2)), if(z0, z1, z2)))), A__LEQ(mark(if(x0, x1, x2)), mark(if(z0, z1, z2))), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), diff(z0, z1)) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), a__diff(mark(z0), mark(z1))), 0, s(diff(p(if(x0, x1, x2)), diff(z0, z1)))), A__LEQ(mark(if(x0, x1, x2)), mark(diff(z0, z1))), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), 0) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), 0), 0, s(diff(p(if(x0, x1, x2)), 0))), A__LEQ(mark(if(x0, x1, x2)), mark(0)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), s(z0)) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), s(mark(z0))), 0, s(diff(p(if(x0, x1, x2)), s(z0)))), A__LEQ(mark(if(x0, x1, x2)), mark(s(z0))), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), true) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), true), 0, s(diff(p(if(x0, x1, x2)), true))), A__LEQ(mark(if(x0, x1, x2)), mark(true)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, x1, x2), false) -> c11(A__IF(a__leq(a__if(mark(x0), x1, x2), false), 0, s(diff(p(if(x0, x1, x2)), false))), A__LEQ(mark(if(x0, x1, x2)), mark(false)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, z1, z2), x3) -> c11(A__IF(a__leq(if(mark(x0), z1, z2), mark(x3)), 0, s(diff(p(if(x0, z1, z2)), x3))), A__LEQ(mark(if(x0, z1, z2)), mark(x3)), MARK(if(x0, z1, z2)))
   A__DIFF(if(p(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__p(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(p(z0), x1, x2)), x3))), A__LEQ(mark(if(p(z0), x1, x2)), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__DIFF(if(leq(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(leq(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(leq(z0, z1), x1, x2)), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__DIFF(if(if(z0, z1, z2), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), 0, s(diff(p(if(if(z0, z1, z2), x1, x2)), x3))), A__LEQ(mark(if(if(z0, z1, z2), x1, x2)), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__DIFF(if(diff(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(diff(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(diff(z0, z1), x1, x2)), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__DIFF(if(0, x1, x2), x3) -> c11(A__IF(a__leq(a__if(0, x1, x2), mark(x3)), 0, s(diff(p(if(0, x1, x2)), x3))), A__LEQ(mark(if(0, x1, x2)), mark(x3)), MARK(if(0, x1, x2)))
   A__DIFF(if(s(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(s(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(s(z0), x1, x2)), x3))), A__LEQ(mark(if(s(z0), x1, x2)), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__DIFF(if(true, x1, x2), x3) -> c11(A__IF(a__leq(a__if(true, x1, x2), mark(x3)), 0, s(diff(p(if(true, x1, x2)), x3))), A__LEQ(mark(if(true, x1, x2)), mark(x3)), MARK(if(true, x1, x2)))
   A__DIFF(if(false, x1, x2), x3) -> c11(A__IF(a__leq(a__if(false, x1, x2), mark(x3)), 0, s(diff(p(if(false, x1, x2)), x3))), A__LEQ(mark(if(false, x1, x2)), mark(x3)), MARK(if(false, x1, x2)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)))

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

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
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   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__IF(leq(a__if(mark(x0), x1, x2), mark(x3)), 0, s(diff(p(if(x0, x1, x2)), x3))), A__LEQ(mark(if(x0, x1, x2)), mark(x3)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, z1, z2), x3) -> c11(A__IF(a__leq(if(mark(x0), z1, z2), mark(x3)), 0, s(diff(p(if(x0, z1, z2)), x3))), A__LEQ(mark(if(x0, z1, z2)), mark(x3)), MARK(if(x0, z1, z2)))
   A__DIFF(if(p(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__p(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(p(z0), x1, x2)), x3))), A__LEQ(mark(if(p(z0), x1, x2)), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__DIFF(if(leq(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(leq(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(leq(z0, z1), x1, x2)), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__DIFF(if(if(z0, z1, z2), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), 0, s(diff(p(if(if(z0, z1, z2), x1, x2)), x3))), A__LEQ(mark(if(if(z0, z1, z2), x1, x2)), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__DIFF(if(diff(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(diff(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(diff(z0, z1), x1, x2)), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__DIFF(if(0, x1, x2), x3) -> c11(A__IF(a__leq(a__if(0, x1, x2), mark(x3)), 0, s(diff(p(if(0, x1, x2)), x3))), A__LEQ(mark(if(0, x1, x2)), mark(x3)), MARK(if(0, x1, x2)))
   A__DIFF(if(s(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(s(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(s(z0), x1, x2)), x3))), A__LEQ(mark(if(s(z0), x1, x2)), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__DIFF(if(true, x1, x2), x3) -> c11(A__IF(a__leq(a__if(true, x1, x2), mark(x3)), 0, s(diff(p(if(true, x1, x2)), x3))), A__LEQ(mark(if(true, x1, x2)), mark(x3)), MARK(if(true, x1, x2)))
   A__DIFF(if(false, x1, x2), x3) -> c11(A__IF(a__leq(a__if(false, x1, x2), mark(x3)), 0, s(diff(p(if(false, x1, x2)), x3))), A__LEQ(mark(if(false, x1, x2)), mark(x3)), MARK(if(false, x1, x2)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
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   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c5(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(leq(p(z0), x1)))
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   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(leq(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(leq(x1, if(z0, z1, z2))))
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   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(leq(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(leq(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(leq(diff(z0, z1), x2)))
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   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(x1, x2)))
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   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c6(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(if(leq(z0, z1), x2, x3)))
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   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
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   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__IF(leq(a__if(mark(x0), x1, x2), mark(x3)), 0, s(diff(p(if(x0, x1, x2)), x3))), A__LEQ(mark(if(x0, x1, x2)), mark(x3)), MARK(if(x0, x1, x2)))
   A__DIFF(if(x0, z1, z2), x3) -> c11(A__IF(a__leq(if(mark(x0), z1, z2), mark(x3)), 0, s(diff(p(if(x0, z1, z2)), x3))), A__LEQ(mark(if(x0, z1, z2)), mark(x3)), MARK(if(x0, z1, z2)))
   A__DIFF(if(p(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__p(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(p(z0), x1, x2)), x3))), A__LEQ(mark(if(p(z0), x1, x2)), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__DIFF(if(leq(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(leq(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(leq(z0, z1), x1, x2)), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__DIFF(if(if(z0, z1, z2), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), 0, s(diff(p(if(if(z0, z1, z2), x1, x2)), x3))), A__LEQ(mark(if(if(z0, z1, z2), x1, x2)), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__DIFF(if(diff(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(diff(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(diff(z0, z1), x1, x2)), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__DIFF(if(0, x1, x2), x3) -> c11(A__IF(a__leq(a__if(0, x1, x2), mark(x3)), 0, s(diff(p(if(0, x1, x2)), x3))), A__LEQ(mark(if(0, x1, x2)), mark(x3)), MARK(if(0, x1, x2)))
   A__DIFF(if(s(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(s(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(s(z0), x1, x2)), x3))), A__LEQ(mark(if(s(z0), x1, x2)), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__DIFF(if(true, x1, x2), x3) -> c11(A__IF(a__leq(a__if(true, x1, x2), mark(x3)), 0, s(diff(p(if(true, x1, x2)), x3))), A__LEQ(mark(if(true, x1, x2)), mark(x3)), MARK(if(true, x1, x2)))
   A__DIFF(if(false, x1, x2), x3) -> c11(A__IF(a__leq(a__if(false, x1, x2), mark(x3)), 0, s(diff(p(if(false, x1, x2)), x3))), A__LEQ(mark(if(false, x1, x2)), mark(x3)), MARK(if(false, x1, x2)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1


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

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

(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__p(0) -> 0
   a__p(s(z0)) -> mark(z0)
   a__p(z0) -> p(z0)
   a__leq(0, z0) -> true
   a__leq(s(z0), 0) -> false
   a__leq(s(z0), s(z1)) -> a__leq(mark(z0), mark(z1))
   a__leq(z0, z1) -> leq(z0, z1)
   a__if(true, z0, z1) -> mark(z0)
   a__if(false, z0, z1) -> mark(z1)
   a__if(z0, z1, z2) -> if(z0, z1, z2)
   a__diff(z0, z1) -> a__if(a__leq(mark(z0), mark(z1)), 0, s(diff(p(z0), z1)))
   a__diff(z0, z1) -> diff(z0, z1)
   mark(p(z0)) -> a__p(mark(z0))
   mark(leq(z0, z1)) -> a__leq(mark(z0), mark(z1))
   mark(if(z0, z1, z2)) -> a__if(mark(z0), z1, z2)
   mark(diff(z0, z1)) -> a__diff(mark(z0), mark(z1))
   mark(0) -> 0
   mark(s(z0)) -> s(mark(z0))
   mark(true) -> true
   mark(false) -> false
Tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(s(0))) -> c5(A__LEQ(mark(x0), s(0)), MARK(x0))
   A__LEQ(s(x0), s(s(s(z0)))) -> c5(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(true))) -> c5(A__LEQ(mark(x0), s(true)), MARK(x0))
   A__LEQ(s(x0), s(s(false))) -> c5(A__LEQ(mark(x0), s(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(s(x1))) -> c5(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(diff(z0, z1)))
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   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(false), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(s(p(z0)))) -> c6(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(s(p(z0))))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(if(x0, z1, z2), x3) -> c11(A__IF(a__leq(if(mark(x0), z1, z2), mark(x3)), 0, s(diff(p(if(x0, z1, z2)), x3))), A__LEQ(mark(if(x0, z1, z2)), mark(x3)), MARK(if(x0, z1, z2)))
   A__DIFF(if(p(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__p(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(p(z0), x1, x2)), x3))), A__LEQ(mark(if(p(z0), x1, x2)), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__DIFF(if(leq(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(leq(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(leq(z0, z1), x1, x2)), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__DIFF(if(if(z0, z1, z2), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), 0, s(diff(p(if(if(z0, z1, z2), x1, x2)), x3))), A__LEQ(mark(if(if(z0, z1, z2), x1, x2)), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__DIFF(if(diff(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(diff(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(diff(z0, z1), x1, x2)), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__DIFF(if(s(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(s(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(s(z0), x1, x2)), x3))), A__LEQ(mark(if(s(z0), x1, x2)), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__DIFF(if(true, x1, x2), x3) -> c11(A__IF(a__leq(a__if(true, x1, x2), mark(x3)), 0, s(diff(p(if(true, x1, x2)), x3))), A__LEQ(mark(if(true, x1, x2)), mark(x3)), MARK(if(true, x1, x2)))
   A__DIFF(if(false, x1, x2), x3) -> c11(A__IF(a__leq(a__if(false, x1, x2), mark(x3)), 0, s(diff(p(if(false, x1, x2)), x3))), A__LEQ(mark(if(false, x1, x2)), mark(x3)), MARK(if(false, x1, x2)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)), MARK(if(x0, x1, x2)))
   A__DIFF(if(0, x1, x2), x3) -> c11(A__IF(a__leq(a__if(0, x1, x2), mark(x3)), 0, s(diff(p(if(0, x1, x2)), x3))), A__LEQ(mark(if(0, x1, x2)), mark(x3)))
S tuples:
   A__P(s(z0)) -> c1(MARK(z0))
   A__IF(true, z0, z1) -> c8(MARK(z0))
   A__IF(false, z0, z1) -> c9(MARK(z1))
   MARK(diff(z0, z1)) -> c18(A__DIFF(mark(z0), mark(z1)), MARK(z0))
   MARK(diff(z0, z1)) -> c19(A__DIFF(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c21(MARK(z0))
   A__LEQ(s(x0), s(0)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(true)) -> c5(MARK(x0))
   A__LEQ(s(x0), s(false)) -> c5(MARK(x0))
   A__LEQ(s(0), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(true), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(false), s(x1)) -> c6(MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), x1) -> c11(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(s(z0)))
   A__DIFF(x0, x1) -> c11(A__LEQ(mark(x0), mark(x1)), MARK(x0))
   A__DIFF(0, x1) -> c11(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)))
   A__DIFF(true, x1) -> c11(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)))
   A__DIFF(false, x1) -> c11(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)))
   A__DIFF(x0, p(z0)) -> c12(A__IF(a__leq(mark(x0), a__p(mark(z0))), 0, s(diff(p(x0), p(z0)))), A__LEQ(mark(x0), mark(p(z0))), MARK(p(z0)))
   A__DIFF(x0, leq(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), 0, s(diff(p(x0), leq(z0, z1)))), A__LEQ(mark(x0), mark(leq(z0, z1))), MARK(leq(z0, z1)))
   A__DIFF(x0, if(z0, z1, z2)) -> c12(A__IF(a__leq(mark(x0), a__if(mark(z0), z1, z2)), 0, s(diff(p(x0), if(z0, z1, z2)))), A__LEQ(mark(x0), mark(if(z0, z1, z2))), MARK(if(z0, z1, z2)))
   A__DIFF(x0, diff(z0, z1)) -> c12(A__IF(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), 0, s(diff(p(x0), diff(z0, z1)))), A__LEQ(mark(x0), mark(diff(z0, z1))), MARK(diff(z0, z1)))
   A__DIFF(x0, s(z0)) -> c12(A__IF(a__leq(mark(x0), s(mark(z0))), 0, s(diff(p(x0), s(z0)))), A__LEQ(mark(x0), mark(s(z0))), MARK(s(z0)))
   A__DIFF(p(z0), x1) -> c12(A__IF(a__leq(a__p(mark(z0)), mark(x1)), 0, s(diff(p(p(z0)), x1))), A__LEQ(mark(p(z0)), mark(x1)), MARK(x1))
   A__DIFF(leq(z0, z1), x1) -> c12(A__IF(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(leq(z0, z1)), x1))), A__LEQ(mark(leq(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(if(z0, z1, z2), x1) -> c12(A__IF(a__leq(a__if(mark(z0), z1, z2), mark(x1)), 0, s(diff(p(if(z0, z1, z2)), x1))), A__LEQ(mark(if(z0, z1, z2)), mark(x1)), MARK(x1))
   A__DIFF(diff(z0, z1), x1) -> c12(A__IF(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), 0, s(diff(p(diff(z0, z1)), x1))), A__LEQ(mark(diff(z0, z1)), mark(x1)), MARK(x1))
   A__DIFF(0, x1) -> c12(A__IF(a__leq(0, mark(x1)), 0, s(diff(p(0), x1))), A__LEQ(mark(0), mark(x1)), MARK(x1))
   A__DIFF(s(z0), x1) -> c12(A__IF(a__leq(s(mark(z0)), mark(x1)), 0, s(diff(p(s(z0)), x1))), A__LEQ(mark(s(z0)), mark(x1)), MARK(x1))
   A__DIFF(true, x1) -> c12(A__IF(a__leq(true, mark(x1)), 0, s(diff(p(true), x1))), A__LEQ(mark(true), mark(x1)), MARK(x1))
   A__DIFF(false, x1) -> c12(A__IF(a__leq(false, mark(x1)), 0, s(diff(p(false), x1))), A__LEQ(mark(false), mark(x1)), MARK(x1))
   A__DIFF(x0, x1) -> c12(A__LEQ(mark(x0), mark(x1)), MARK(x1))
   A__DIFF(x0, 0) -> c12(A__IF(a__leq(mark(x0), 0), 0, s(diff(p(x0), 0))), A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, true) -> c12(A__IF(a__leq(mark(x0), true), 0, s(diff(p(x0), true))), A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, false) -> c12(A__IF(a__leq(mark(x0), false), 0, s(diff(p(x0), false))), A__LEQ(mark(x0), mark(false)))
   MARK(p(p(z0))) -> c14(A__P(a__p(mark(z0))), MARK(p(z0)))
   MARK(p(leq(z0, z1))) -> c14(A__P(a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(p(if(z0, z1, z2))) -> c14(A__P(a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(p(diff(z0, z1))) -> c14(A__P(a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(p(s(z0))) -> c14(A__P(s(mark(z0))), MARK(s(z0)))
   MARK(leq(x0, p(z0))) -> c15(A__LEQ(mark(x0), a__p(mark(z0))), MARK(x0))
   MARK(leq(x0, leq(z0, z1))) -> c15(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, if(z0, z1, z2))) -> c15(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(x0))
   MARK(leq(x0, diff(z0, z1))) -> c15(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(x0))
   MARK(leq(x0, s(z0))) -> c15(A__LEQ(mark(x0), s(mark(z0))), MARK(x0))
   MARK(leq(p(z0), x1)) -> c15(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(p(z0)))
   MARK(leq(leq(z0, z1), x1)) -> c15(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(leq(z0, z1)))
   MARK(leq(if(z0, z1, z2), x1)) -> c15(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(if(z0, z1, z2)))
   MARK(leq(diff(z0, z1), x1)) -> c15(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(diff(z0, z1)))
   MARK(leq(s(z0), x1)) -> c15(A__LEQ(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(leq(x0, 0)) -> c15(MARK(x0))
   MARK(leq(x0, true)) -> c15(MARK(x0))
   MARK(leq(x0, false)) -> c15(MARK(x0))
   MARK(leq(x0, p(z0))) -> c16(A__LEQ(mark(x0), a__p(mark(z0))), MARK(p(z0)))
   MARK(leq(x0, leq(z0, z1))) -> c16(A__LEQ(mark(x0), a__leq(mark(z0), mark(z1))), MARK(leq(z0, z1)))
   MARK(leq(x0, if(z0, z1, z2))) -> c16(A__LEQ(mark(x0), a__if(mark(z0), z1, z2)), MARK(if(z0, z1, z2)))
   MARK(leq(x0, diff(z0, z1))) -> c16(A__LEQ(mark(x0), a__diff(mark(z0), mark(z1))), MARK(diff(z0, z1)))
   MARK(leq(x0, s(z0))) -> c16(A__LEQ(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(leq(p(z0), x1)) -> c16(A__LEQ(a__p(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(leq(z0, z1), x1)) -> c16(A__LEQ(a__leq(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(if(z0, z1, z2), x1)) -> c16(A__LEQ(a__if(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(leq(diff(z0, z1), x1)) -> c16(A__LEQ(a__diff(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(leq(s(z0), x1)) -> c16(A__LEQ(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(leq(0, x1)) -> c16(MARK(x1))
   MARK(leq(true, x1)) -> c16(MARK(x1))
   MARK(leq(false, x1)) -> c16(MARK(x1))
   MARK(if(p(z0), x1, x2)) -> c17(A__IF(a__p(mark(z0)), x1, x2), MARK(p(z0)))
   MARK(if(leq(z0, z1), x1, x2)) -> c17(A__IF(a__leq(mark(z0), mark(z1)), x1, x2), MARK(leq(z0, z1)))
   MARK(if(if(z0, z1, z2), x1, x2)) -> c17(A__IF(a__if(mark(z0), z1, z2), x1, x2), MARK(if(z0, z1, z2)))
   MARK(if(diff(z0, z1), x1, x2)) -> c17(A__IF(a__diff(mark(z0), mark(z1)), x1, x2), MARK(diff(z0, z1)))
   MARK(if(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(if(true, x1, x2)) -> c17(A__IF(true, x1, x2))
   MARK(if(false, x1, x2)) -> c17(A__IF(false, x1, x2))
   A__LEQ(s(x0), s(p(p(z0)))) -> c5(A__LEQ(mark(x0), a__p(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__p(a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(p(diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(p(0))) -> c5(A__LEQ(mark(x0), a__p(0)), MARK(x0))
   A__LEQ(s(x0), s(p(s(z0)))) -> c5(A__LEQ(mark(x0), a__p(s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(p(true))) -> c5(A__LEQ(mark(x0), a__p(true)), MARK(x0))
   A__LEQ(s(x0), s(p(false))) -> c5(A__LEQ(mark(x0), a__p(false)), MARK(x0))
   A__LEQ(s(p(z0)), s(p(x1))) -> c5(A__LEQ(a__p(mark(z0)), a__p(mark(x1))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(p(x1))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__p(mark(x1))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(p(x1))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(p(x1))) -> c5(A__LEQ(s(mark(z0)), a__p(mark(x1))), MARK(s(z0)))
   A__LEQ(s(x0), s(p(x1))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(leq(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, 0))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, true))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(leq(x1, false))) -> c5(A__LEQ(mark(x0), a__leq(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(leq(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(0, x2))) -> c5(A__LEQ(mark(x0), a__leq(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__leq(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(true, x2))) -> c5(A__LEQ(mark(x0), a__leq(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(leq(false, x2))) -> c5(A__LEQ(mark(x0), a__leq(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(leq(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(leq(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(leq(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(leq(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__leq(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(leq(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(if(p(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__p(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(leq(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(if(z0, z1, z2), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(diff(z0, z1), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(0, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(s(z0), x2, x3))) -> c5(A__LEQ(mark(x0), a__if(s(mark(z0)), x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(true, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(true, x2, x3)), MARK(x0))
   A__LEQ(s(x0), s(if(false, x2, x3))) -> c5(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(x0))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c5(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(s(z0)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(A__LEQ(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, true))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(x0))
   A__LEQ(s(x0), s(diff(x1, false))) -> c5(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(x0))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c5(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(0, x2))) -> c5(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c5(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(true, x2))) -> c5(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(x0))
   A__LEQ(s(x0), s(diff(false, x2))) -> c5(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(x0))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c5(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(p(z0)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(leq(z0, z1)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c5(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(if(z0, z1, z2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c5(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(z0, z1)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c5(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(s(z0)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c5(MARK(x0))
   A__LEQ(s(x0), s(s(p(z0)))) -> c5(A__LEQ(mark(x0), s(a__p(mark(z0)))), MARK(x0))
   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c5(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(x0))
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   A__LEQ(s(x0), s(if(false, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(false, x2, x3)), MARK(if(false, x2, x3)))
   A__LEQ(s(p(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__p(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(leq(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(if(z0, z1, z2)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(diff(z0, z1)), s(if(x1, x2, x3))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(s(z0)), s(if(x1, x2, x3))) -> c6(A__LEQ(s(mark(z0)), a__if(mark(x1), x2, x3)), MARK(if(x1, x2, x3)))
   A__LEQ(s(x0), s(if(x1, z1, z2))) -> c6(MARK(if(x1, z1, z2)))
   A__LEQ(s(x0), s(if(0, x2, x3))) -> c6(A__LEQ(mark(x0), a__if(0, x2, x3)))
   A__LEQ(s(0), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(true), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
   A__LEQ(s(false), s(if(x1, x2, x3))) -> c6(MARK(if(x1, x2, x3)))
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   A__LEQ(s(x0), s(diff(x1, p(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), MARK(diff(x1, p(z0))))
   A__LEQ(s(x0), s(diff(x1, leq(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), MARK(diff(x1, leq(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), MARK(diff(x1, if(z0, z1, z2))))
   A__LEQ(s(x0), s(diff(x1, diff(z0, z1)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), MARK(diff(x1, diff(z0, z1))))
   A__LEQ(s(x0), s(diff(x1, 0))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), 0)), MARK(diff(x1, 0)))
   A__LEQ(s(x0), s(diff(x1, s(z0)))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), s(mark(z0)))), MARK(diff(x1, s(z0))))
   A__LEQ(s(x0), s(diff(x1, true))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), true)), MARK(diff(x1, true)))
   A__LEQ(s(x0), s(diff(x1, false))) -> c6(A__LEQ(mark(x0), a__diff(mark(x1), false)), MARK(diff(x1, false)))
   A__LEQ(s(x0), s(diff(p(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), MARK(diff(p(z0), x2)))
   A__LEQ(s(x0), s(diff(leq(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), MARK(diff(leq(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(if(z0, z1, z2), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), MARK(diff(if(z0, z1, z2), x2)))
   A__LEQ(s(x0), s(diff(diff(z0, z1), x2))) -> c6(A__LEQ(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), MARK(diff(diff(z0, z1), x2)))
   A__LEQ(s(x0), s(diff(0, x2))) -> c6(A__LEQ(mark(x0), a__diff(0, mark(x2))), MARK(diff(0, x2)))
   A__LEQ(s(x0), s(diff(s(z0), x2))) -> c6(A__LEQ(mark(x0), a__diff(s(mark(z0)), mark(x2))), MARK(diff(s(z0), x2)))
   A__LEQ(s(x0), s(diff(true, x2))) -> c6(A__LEQ(mark(x0), a__diff(true, mark(x2))), MARK(diff(true, x2)))
   A__LEQ(s(x0), s(diff(false, x2))) -> c6(A__LEQ(mark(x0), a__diff(false, mark(x2))), MARK(diff(false, x2)))
   A__LEQ(s(p(z0)), s(diff(x1, x2))) -> c6(A__LEQ(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(leq(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(if(z0, z1, z2)), s(diff(x1, x2))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(diff(z0, z1)), s(diff(x1, x2))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(s(z0)), s(diff(x1, x2))) -> c6(A__LEQ(s(mark(z0)), a__diff(mark(x1), mark(x2))), MARK(diff(x1, x2)))
   A__LEQ(s(x0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(0), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
   A__LEQ(s(true), s(diff(x1, x2))) -> c6(MARK(diff(x1, x2)))
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   A__LEQ(s(x0), s(s(leq(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__leq(mark(z0), mark(z1)))), MARK(s(leq(z0, z1))))
   A__LEQ(s(x0), s(s(if(z0, z1, z2)))) -> c6(A__LEQ(mark(x0), s(a__if(mark(z0), z1, z2))), MARK(s(if(z0, z1, z2))))
   A__LEQ(s(x0), s(s(diff(z0, z1)))) -> c6(A__LEQ(mark(x0), s(a__diff(mark(z0), mark(z1)))), MARK(s(diff(z0, z1))))
   A__LEQ(s(x0), s(s(0))) -> c6(A__LEQ(mark(x0), s(0)), MARK(s(0)))
   A__LEQ(s(x0), s(s(s(z0)))) -> c6(A__LEQ(mark(x0), s(s(mark(z0)))), MARK(s(s(z0))))
   A__LEQ(s(x0), s(s(true))) -> c6(A__LEQ(mark(x0), s(true)), MARK(s(true)))
   A__LEQ(s(x0), s(s(false))) -> c6(A__LEQ(mark(x0), s(false)), MARK(s(false)))
   A__LEQ(s(p(z0)), s(s(x1))) -> c6(A__LEQ(a__p(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(leq(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__leq(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(if(z0, z1, z2)), s(s(x1))) -> c6(A__LEQ(a__if(mark(z0), z1, z2), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(diff(z0, z1)), s(s(x1))) -> c6(A__LEQ(a__diff(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(s(z0)), s(s(x1))) -> c6(A__LEQ(s(mark(z0)), s(mark(x1))), MARK(s(x1)))
   A__LEQ(s(x0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(0), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(true), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(false), s(s(x1))) -> c6(MARK(s(x1)))
   A__LEQ(s(p(p(z0))), s(x1)) -> c6(A__LEQ(a__p(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(leq(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(a__p(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(p(diff(z0, z1))), s(x1)) -> c6(A__LEQ(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(p(0)), s(x1)) -> c6(A__LEQ(a__p(0), mark(x1)), MARK(x1))
   A__LEQ(s(p(s(z0))), s(x1)) -> c6(A__LEQ(a__p(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(p(true)), s(x1)) -> c6(A__LEQ(a__p(true), mark(x1)), MARK(x1))
   A__LEQ(s(p(false)), s(x1)) -> c6(A__LEQ(a__p(false), mark(x1)), MARK(x1))
   A__LEQ(s(p(x0)), s(x1)) -> c6(MARK(x1))
   A__LEQ(s(leq(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, 0)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, true)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, false)), s(x2)) -> c6(A__LEQ(a__leq(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(leq(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(0, x1)), s(x2)) -> c6(A__LEQ(a__leq(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__leq(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(true, x1)), s(x2)) -> c6(A__LEQ(a__leq(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(false, x1)), s(x2)) -> c6(A__LEQ(a__leq(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(leq(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(if(p(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__p(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(leq(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(if(z0, z1, z2), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(diff(z0, z1), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(0, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(0, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(s(z0), x1, x2)), s(x3)) -> c6(A__LEQ(a__if(s(mark(z0)), x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(true, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(true, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(false, x1, x2)), s(x3)) -> c6(A__LEQ(a__if(false, x1, x2), mark(x3)), MARK(x3))
   A__LEQ(s(if(x0, z1, z2)), s(x3)) -> c6(MARK(x3))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(A__LEQ(a__if(a__leq(mark(mark(x0)), mark(mark(x1))), 0, s(diff(p(mark(x0)), mark(x1)))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, p(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__p(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, leq(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, if(z0, z1, z2))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, diff(z0, z1))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, 0)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), 0), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, s(z0))), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), s(mark(z0))), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, true)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), true), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, false)), s(x2)) -> c6(A__LEQ(a__diff(mark(x0), false), mark(x2)), MARK(x2))
   A__LEQ(s(diff(p(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__p(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(leq(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(if(z0, z1, z2), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(diff(z0, z1), x1)), s(x2)) -> c6(A__LEQ(a__diff(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(0, x1)), s(x2)) -> c6(A__LEQ(a__diff(0, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(s(z0), x1)), s(x2)) -> c6(A__LEQ(a__diff(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(true, x1)), s(x2)) -> c6(A__LEQ(a__diff(true, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(false, x1)), s(x2)) -> c6(A__LEQ(a__diff(false, mark(x1)), mark(x2)), MARK(x2))
   A__LEQ(s(diff(x0, x1)), s(x2)) -> c6(MARK(x2))
   A__LEQ(s(s(p(z0))), s(x1)) -> c6(A__LEQ(s(a__p(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(leq(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__leq(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(if(z0, z1, z2))), s(x1)) -> c6(A__LEQ(s(a__if(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__LEQ(s(s(diff(z0, z1))), s(x1)) -> c6(A__LEQ(s(a__diff(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__LEQ(s(s(0)), s(x1)) -> c6(A__LEQ(s(0), mark(x1)), MARK(x1))
   A__LEQ(s(s(s(z0))), s(x1)) -> c6(A__LEQ(s(s(mark(z0))), mark(x1)), MARK(x1))
   A__LEQ(s(s(true)), s(x1)) -> c6(A__LEQ(s(true), mark(x1)), MARK(x1))
   A__LEQ(s(s(false)), s(x1)) -> c6(A__LEQ(s(false), mark(x1)), MARK(x1))
   A__DIFF(x0, p(x1)) -> c11(A__IF(a__leq(mark(x0), p(mark(x1))), 0, s(diff(p(x0), p(x1)))), A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(x0, p(p(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(a__p(mark(z0)))), 0, s(diff(p(x0), p(p(z0))))), A__LEQ(mark(x0), mark(p(p(z0)))), MARK(x0))
   A__DIFF(x0, p(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(leq(z0, z1))))), A__LEQ(mark(x0), mark(p(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__p(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), p(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(p(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, p(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__p(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), p(diff(z0, z1))))), A__LEQ(mark(x0), mark(p(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, p(0)) -> c11(A__IF(a__leq(mark(x0), a__p(0)), 0, s(diff(p(x0), p(0)))), A__LEQ(mark(x0), mark(p(0))), MARK(x0))
   A__DIFF(x0, p(s(z0))) -> c11(A__IF(a__leq(mark(x0), a__p(s(mark(z0)))), 0, s(diff(p(x0), p(s(z0))))), A__LEQ(mark(x0), mark(p(s(z0)))), MARK(x0))
   A__DIFF(x0, p(true)) -> c11(A__IF(a__leq(mark(x0), a__p(true)), 0, s(diff(p(x0), p(true)))), A__LEQ(mark(x0), mark(p(true))), MARK(x0))
   A__DIFF(x0, p(false)) -> c11(A__IF(a__leq(mark(x0), a__p(false)), 0, s(diff(p(x0), p(false)))), A__LEQ(mark(x0), mark(p(false))), MARK(x0))
   A__DIFF(p(z0), p(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__p(mark(x1))), 0, s(diff(p(p(z0)), p(x1)))), A__LEQ(mark(p(z0)), mark(p(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(leq(z0, z1)), p(x1)))), A__LEQ(mark(leq(z0, z1)), mark(p(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), p(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__p(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), p(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(p(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), p(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__p(mark(x1))), 0, s(diff(p(diff(z0, z1)), p(x1)))), A__LEQ(mark(diff(z0, z1)), mark(p(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), p(x1)) -> c11(A__IF(a__leq(s(mark(z0)), a__p(mark(x1))), 0, s(diff(p(s(z0)), p(x1)))), A__LEQ(mark(s(z0)), mark(p(x1))), MARK(s(z0)))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))))
   A__DIFF(x0, p(x1)) -> c11(A__LEQ(mark(x0), mark(p(x1))), MARK(x0))
   A__DIFF(0, p(x1)) -> c11(A__IF(a__leq(0, a__p(mark(x1))), 0, s(diff(p(0), p(x1)))), A__LEQ(mark(0), mark(p(x1))))
   A__DIFF(true, p(x1)) -> c11(A__IF(a__leq(true, a__p(mark(x1))), 0, s(diff(p(true), p(x1)))), A__LEQ(mark(true), mark(p(x1))))
   A__DIFF(false, p(x1)) -> c11(A__IF(a__leq(false, a__p(mark(x1))), 0, s(diff(p(false), p(x1)))), A__LEQ(mark(false), mark(p(x1))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__IF(a__leq(mark(x0), leq(mark(x1), mark(x2))), 0, s(diff(p(x0), leq(x1, x2)))), A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(x0, leq(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), leq(x1, p(z0))))), A__LEQ(mark(x0), mark(leq(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), leq(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(leq(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, leq(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), leq(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(leq(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, leq(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), 0)), 0, s(diff(p(x0), leq(x1, 0)))), A__LEQ(mark(x0), mark(leq(x1, 0))), MARK(x0))
   A__DIFF(x0, leq(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), leq(x1, s(z0))))), A__LEQ(mark(x0), mark(leq(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, leq(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), true)), 0, s(diff(p(x0), leq(x1, true)))), A__LEQ(mark(x0), mark(leq(x1, true))), MARK(x0))
   A__DIFF(x0, leq(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__leq(mark(x1), false)), 0, s(diff(p(x0), leq(x1, false)))), A__LEQ(mark(x0), mark(leq(x1, false))), MARK(x0))
   A__DIFF(x0, leq(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(p(z0), x2)))), A__LEQ(mark(x0), mark(leq(p(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), leq(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(leq(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, leq(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), leq(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(leq(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, leq(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(0, mark(x2))), 0, s(diff(p(x0), leq(0, x2)))), A__LEQ(mark(x0), mark(leq(0, x2))), MARK(x0))
   A__DIFF(x0, leq(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), leq(s(z0), x2)))), A__LEQ(mark(x0), mark(leq(s(z0), x2))), MARK(x0))
   A__DIFF(x0, leq(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(true, mark(x2))), 0, s(diff(p(x0), leq(true, x2)))), A__LEQ(mark(x0), mark(leq(true, x2))), MARK(x0))
   A__DIFF(x0, leq(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__leq(false, mark(x2))), 0, s(diff(p(x0), leq(false, x2)))), A__LEQ(mark(x0), mark(leq(false, x2))), MARK(x0))
   A__DIFF(p(z0), leq(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), leq(x1, x2)))), A__LEQ(mark(p(z0)), mark(leq(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), leq(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(leq(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), leq(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__leq(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), leq(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(leq(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), leq(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), leq(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(leq(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), leq(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__leq(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), leq(x1, x2)))), A__LEQ(mark(s(z0)), mark(leq(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))))
   A__DIFF(x0, leq(x1, x2)) -> c11(A__LEQ(mark(x0), mark(leq(x1, x2))), MARK(x0))
   A__DIFF(0, leq(x1, x2)) -> c11(A__IF(a__leq(0, a__leq(mark(x1), mark(x2))), 0, s(diff(p(0), leq(x1, x2)))), A__LEQ(mark(0), mark(leq(x1, x2))))
   A__DIFF(true, leq(x1, x2)) -> c11(A__IF(a__leq(true, a__leq(mark(x1), mark(x2))), 0, s(diff(p(true), leq(x1, x2)))), A__LEQ(mark(true), mark(leq(x1, x2))))
   A__DIFF(false, leq(x1, x2)) -> c11(A__IF(a__leq(false, a__leq(mark(x1), mark(x2))), 0, s(diff(p(false), leq(x1, x2)))), A__LEQ(mark(false), mark(leq(x1, x2))))
   A__DIFF(x0, if(x1, z1, z2)) -> c11(A__IF(a__leq(mark(x0), if(mark(x1), z1, z2)), 0, s(diff(p(x0), if(x1, z1, z2)))), A__LEQ(mark(x0), mark(if(x1, z1, z2))), MARK(x0))
   A__DIFF(x0, if(p(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__p(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(p(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(p(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(leq(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(leq(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(leq(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(if(z0, z1, z2), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__if(mark(z0), z1, z2), x2, x3)), 0, s(diff(p(x0), if(if(z0, z1, z2), x2, x3)))), A__LEQ(mark(x0), mark(if(if(z0, z1, z2), x2, x3))), MARK(x0))
   A__DIFF(x0, if(diff(z0, z1), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(a__diff(mark(z0), mark(z1)), x2, x3)), 0, s(diff(p(x0), if(diff(z0, z1), x2, x3)))), A__LEQ(mark(x0), mark(if(diff(z0, z1), x2, x3))), MARK(x0))
   A__DIFF(x0, if(0, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(0, x2, x3)), 0, s(diff(p(x0), if(0, x2, x3)))), A__LEQ(mark(x0), mark(if(0, x2, x3))), MARK(x0))
   A__DIFF(x0, if(s(z0), x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(s(mark(z0)), x2, x3)), 0, s(diff(p(x0), if(s(z0), x2, x3)))), A__LEQ(mark(x0), mark(if(s(z0), x2, x3))), MARK(x0))
   A__DIFF(x0, if(true, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(true, x2, x3)), 0, s(diff(p(x0), if(true, x2, x3)))), A__LEQ(mark(x0), mark(if(true, x2, x3))), MARK(x0))
   A__DIFF(x0, if(false, x2, x3)) -> c11(A__IF(a__leq(mark(x0), a__if(false, x2, x3)), 0, s(diff(p(x0), if(false, x2, x3)))), A__LEQ(mark(x0), mark(if(false, x2, x3))), MARK(x0))
   A__DIFF(p(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(p(z0)), if(x1, x2, x3)))), A__LEQ(mark(p(z0)), mark(if(x1, x2, x3))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(leq(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(leq(z0, z1)), mark(if(x1, x2, x3))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__if(mark(x1), x2, x3)), 0, s(diff(p(if(z0, z1, z2)), if(x1, x2, x3)))), A__LEQ(mark(if(z0, z1, z2)), mark(if(x1, x2, x3))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), if(x1, x2, x3)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__if(mark(x1), x2, x3)), 0, s(diff(p(diff(z0, z1)), if(x1, x2, x3)))), A__LEQ(mark(diff(z0, z1)), mark(if(x1, x2, x3))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), if(x1, x2, x3)) -> c11(A__IF(a__leq(s(mark(z0)), a__if(mark(x1), x2, x3)), 0, s(diff(p(s(z0)), if(x1, x2, x3)))), A__LEQ(mark(s(z0)), mark(if(x1, x2, x3))), MARK(s(z0)))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))))
   A__DIFF(x0, if(x1, x2, x3)) -> c11(A__LEQ(mark(x0), mark(if(x1, x2, x3))), MARK(x0))
   A__DIFF(0, if(x1, x2, x3)) -> c11(A__IF(a__leq(0, a__if(mark(x1), x2, x3)), 0, s(diff(p(0), if(x1, x2, x3)))), A__LEQ(mark(0), mark(if(x1, x2, x3))))
   A__DIFF(true, if(x1, x2, x3)) -> c11(A__IF(a__leq(true, a__if(mark(x1), x2, x3)), 0, s(diff(p(true), if(x1, x2, x3)))), A__LEQ(mark(true), mark(if(x1, x2, x3))))
   A__DIFF(false, if(x1, x2, x3)) -> c11(A__IF(a__leq(false, a__if(mark(x1), x2, x3)), 0, s(diff(p(false), if(x1, x2, x3)))), A__LEQ(mark(false), mark(if(x1, x2, x3))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), a__if(a__leq(mark(mark(x1)), mark(mark(x2))), 0, s(diff(p(mark(x1)), mark(x2))))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__IF(a__leq(mark(x0), diff(mark(x1), mark(x2))), 0, s(diff(p(x0), diff(x1, x2)))), A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(x0, diff(x1, p(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__p(mark(z0)))), 0, s(diff(p(x0), diff(x1, p(z0))))), A__LEQ(mark(x0), mark(diff(x1, p(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, leq(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), diff(x1, if(z0, z1, z2))))), A__LEQ(mark(x0), mark(diff(x1, if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, diff(x1, diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), diff(x1, diff(z0, z1))))), A__LEQ(mark(x0), mark(diff(x1, diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, diff(x1, 0)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), 0)), 0, s(diff(p(x0), diff(x1, 0)))), A__LEQ(mark(x0), mark(diff(x1, 0))), MARK(x0))
   A__DIFF(x0, diff(x1, s(z0))) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), s(mark(z0)))), 0, s(diff(p(x0), diff(x1, s(z0))))), A__LEQ(mark(x0), mark(diff(x1, s(z0)))), MARK(x0))
   A__DIFF(x0, diff(x1, true)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), true)), 0, s(diff(p(x0), diff(x1, true)))), A__LEQ(mark(x0), mark(diff(x1, true))), MARK(x0))
   A__DIFF(x0, diff(x1, false)) -> c11(A__IF(a__leq(mark(x0), a__diff(mark(x1), false)), 0, s(diff(p(x0), diff(x1, false)))), A__LEQ(mark(x0), mark(diff(x1, false))), MARK(x0))
   A__DIFF(x0, diff(p(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__p(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(p(z0), x2)))), A__LEQ(mark(x0), mark(diff(p(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(leq(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__leq(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(leq(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(leq(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(if(z0, z1, z2), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__if(mark(z0), z1, z2), mark(x2))), 0, s(diff(p(x0), diff(if(z0, z1, z2), x2)))), A__LEQ(mark(x0), mark(diff(if(z0, z1, z2), x2))), MARK(x0))
   A__DIFF(x0, diff(diff(z0, z1), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(a__diff(mark(z0), mark(z1)), mark(x2))), 0, s(diff(p(x0), diff(diff(z0, z1), x2)))), A__LEQ(mark(x0), mark(diff(diff(z0, z1), x2))), MARK(x0))
   A__DIFF(x0, diff(0, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(0, mark(x2))), 0, s(diff(p(x0), diff(0, x2)))), A__LEQ(mark(x0), mark(diff(0, x2))), MARK(x0))
   A__DIFF(x0, diff(s(z0), x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(s(mark(z0)), mark(x2))), 0, s(diff(p(x0), diff(s(z0), x2)))), A__LEQ(mark(x0), mark(diff(s(z0), x2))), MARK(x0))
   A__DIFF(x0, diff(true, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(true, mark(x2))), 0, s(diff(p(x0), diff(true, x2)))), A__LEQ(mark(x0), mark(diff(true, x2))), MARK(x0))
   A__DIFF(x0, diff(false, x2)) -> c11(A__IF(a__leq(mark(x0), a__diff(false, mark(x2))), 0, s(diff(p(x0), diff(false, x2)))), A__LEQ(mark(x0), mark(diff(false, x2))), MARK(x0))
   A__DIFF(p(z0), diff(x1, x2)) -> c11(A__IF(a__leq(a__p(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(p(z0)), diff(x1, x2)))), A__LEQ(mark(p(z0)), mark(diff(x1, x2))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(leq(z0, z1)), diff(x1, x2)))), A__LEQ(mark(leq(z0, z1)), mark(diff(x1, x2))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), diff(x1, x2)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), a__diff(mark(x1), mark(x2))), 0, s(diff(p(if(z0, z1, z2)), diff(x1, x2)))), A__LEQ(mark(if(z0, z1, z2)), mark(diff(x1, x2))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), diff(x1, x2)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(diff(z0, z1)), diff(x1, x2)))), A__LEQ(mark(diff(z0, z1)), mark(diff(x1, x2))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), diff(x1, x2)) -> c11(A__IF(a__leq(s(mark(z0)), a__diff(mark(x1), mark(x2))), 0, s(diff(p(s(z0)), diff(x1, x2)))), A__LEQ(mark(s(z0)), mark(diff(x1, x2))), MARK(s(z0)))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))))
   A__DIFF(x0, diff(x1, x2)) -> c11(A__LEQ(mark(x0), mark(diff(x1, x2))), MARK(x0))
   A__DIFF(0, diff(x1, x2)) -> c11(A__IF(a__leq(0, a__diff(mark(x1), mark(x2))), 0, s(diff(p(0), diff(x1, x2)))), A__LEQ(mark(0), mark(diff(x1, x2))))
   A__DIFF(true, diff(x1, x2)) -> c11(A__IF(a__leq(true, a__diff(mark(x1), mark(x2))), 0, s(diff(p(true), diff(x1, x2)))), A__LEQ(mark(true), mark(diff(x1, x2))))
   A__DIFF(false, diff(x1, x2)) -> c11(A__IF(a__leq(false, a__diff(mark(x1), mark(x2))), 0, s(diff(p(false), diff(x1, x2)))), A__LEQ(mark(false), mark(diff(x1, x2))))
   A__DIFF(p(z0), 0) -> c11(A__IF(a__leq(a__p(mark(z0)), 0), 0, s(diff(p(p(z0)), 0))), A__LEQ(mark(p(z0)), mark(0)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), 0) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), 0), 0, s(diff(p(leq(z0, z1)), 0))), A__LEQ(mark(leq(z0, z1)), mark(0)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), 0) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), 0), 0, s(diff(p(if(z0, z1, z2)), 0))), A__LEQ(mark(if(z0, z1, z2)), mark(0)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), 0) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), 0), 0, s(diff(p(diff(z0, z1)), 0))), A__LEQ(mark(diff(z0, z1)), mark(0)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), 0) -> c11(A__IF(a__leq(s(mark(z0)), 0), 0, s(diff(p(s(z0)), 0))), A__LEQ(mark(s(z0)), mark(0)), MARK(s(z0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)))
   A__DIFF(x0, 0) -> c11(A__LEQ(mark(x0), mark(0)), MARK(x0))
   A__DIFF(0, 0) -> c11(A__IF(a__leq(0, 0), 0, s(diff(p(0), 0))), A__LEQ(mark(0), mark(0)))
   A__DIFF(true, 0) -> c11(A__IF(a__leq(true, 0), 0, s(diff(p(true), 0))), A__LEQ(mark(true), mark(0)))
   A__DIFF(false, 0) -> c11(A__IF(a__leq(false, 0), 0, s(diff(p(false), 0))), A__LEQ(mark(false), mark(0)))
   A__DIFF(x0, s(p(z0))) -> c11(A__IF(a__leq(mark(x0), s(a__p(mark(z0)))), 0, s(diff(p(x0), s(p(z0))))), A__LEQ(mark(x0), mark(s(p(z0)))), MARK(x0))
   A__DIFF(x0, s(leq(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__leq(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(leq(z0, z1))))), A__LEQ(mark(x0), mark(s(leq(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(if(z0, z1, z2))) -> c11(A__IF(a__leq(mark(x0), s(a__if(mark(z0), z1, z2))), 0, s(diff(p(x0), s(if(z0, z1, z2))))), A__LEQ(mark(x0), mark(s(if(z0, z1, z2)))), MARK(x0))
   A__DIFF(x0, s(diff(z0, z1))) -> c11(A__IF(a__leq(mark(x0), s(a__diff(mark(z0), mark(z1)))), 0, s(diff(p(x0), s(diff(z0, z1))))), A__LEQ(mark(x0), mark(s(diff(z0, z1)))), MARK(x0))
   A__DIFF(x0, s(0)) -> c11(A__IF(a__leq(mark(x0), s(0)), 0, s(diff(p(x0), s(0)))), A__LEQ(mark(x0), mark(s(0))), MARK(x0))
   A__DIFF(x0, s(s(z0))) -> c11(A__IF(a__leq(mark(x0), s(s(mark(z0)))), 0, s(diff(p(x0), s(s(z0))))), A__LEQ(mark(x0), mark(s(s(z0)))), MARK(x0))
   A__DIFF(x0, s(true)) -> c11(A__IF(a__leq(mark(x0), s(true)), 0, s(diff(p(x0), s(true)))), A__LEQ(mark(x0), mark(s(true))), MARK(x0))
   A__DIFF(x0, s(false)) -> c11(A__IF(a__leq(mark(x0), s(false)), 0, s(diff(p(x0), s(false)))), A__LEQ(mark(x0), mark(s(false))), MARK(x0))
   A__DIFF(p(z0), s(x1)) -> c11(A__IF(a__leq(a__p(mark(z0)), s(mark(x1))), 0, s(diff(p(p(z0)), s(x1)))), A__LEQ(mark(p(z0)), mark(s(x1))), MARK(p(z0)))
   A__DIFF(leq(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(leq(z0, z1)), s(x1)))), A__LEQ(mark(leq(z0, z1)), mark(s(x1))), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), s(x1)) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), s(mark(x1))), 0, s(diff(p(if(z0, z1, z2)), s(x1)))), A__LEQ(mark(if(z0, z1, z2)), mark(s(x1))), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), s(x1)) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), s(mark(x1))), 0, s(diff(p(diff(z0, z1)), s(x1)))), A__LEQ(mark(diff(z0, z1)), mark(s(x1))), MARK(diff(z0, z1)))
   A__DIFF(s(z0), s(x1)) -> c11(A__IF(a__leq(s(mark(z0)), s(mark(x1))), 0, s(diff(p(s(z0)), s(x1)))), A__LEQ(mark(s(z0)), mark(s(x1))), MARK(s(z0)))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))))
   A__DIFF(x0, s(x1)) -> c11(A__LEQ(mark(x0), mark(s(x1))), MARK(x0))
   A__DIFF(0, s(x1)) -> c11(A__IF(a__leq(0, s(mark(x1))), 0, s(diff(p(0), s(x1)))), A__LEQ(mark(0), mark(s(x1))))
   A__DIFF(true, s(x1)) -> c11(A__IF(a__leq(true, s(mark(x1))), 0, s(diff(p(true), s(x1)))), A__LEQ(mark(true), mark(s(x1))))
   A__DIFF(false, s(x1)) -> c11(A__IF(a__leq(false, s(mark(x1))), 0, s(diff(p(false), s(x1)))), A__LEQ(mark(false), mark(s(x1))))
   A__DIFF(p(z0), true) -> c11(A__IF(a__leq(a__p(mark(z0)), true), 0, s(diff(p(p(z0)), true))), A__LEQ(mark(p(z0)), mark(true)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), true) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), true), 0, s(diff(p(leq(z0, z1)), true))), A__LEQ(mark(leq(z0, z1)), mark(true)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), true) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), true), 0, s(diff(p(if(z0, z1, z2)), true))), A__LEQ(mark(if(z0, z1, z2)), mark(true)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), true) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), true), 0, s(diff(p(diff(z0, z1)), true))), A__LEQ(mark(diff(z0, z1)), mark(true)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), true) -> c11(A__IF(a__leq(s(mark(z0)), true), 0, s(diff(p(s(z0)), true))), A__LEQ(mark(s(z0)), mark(true)), MARK(s(z0)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)))
   A__DIFF(x0, true) -> c11(A__LEQ(mark(x0), mark(true)), MARK(x0))
   A__DIFF(0, true) -> c11(A__IF(a__leq(0, true), 0, s(diff(p(0), true))), A__LEQ(mark(0), mark(true)))
   A__DIFF(true, true) -> c11(A__IF(a__leq(true, true), 0, s(diff(p(true), true))), A__LEQ(mark(true), mark(true)))
   A__DIFF(false, true) -> c11(A__IF(a__leq(false, true), 0, s(diff(p(false), true))), A__LEQ(mark(false), mark(true)))
   A__DIFF(p(z0), false) -> c11(A__IF(a__leq(a__p(mark(z0)), false), 0, s(diff(p(p(z0)), false))), A__LEQ(mark(p(z0)), mark(false)), MARK(p(z0)))
   A__DIFF(leq(z0, z1), false) -> c11(A__IF(a__leq(a__leq(mark(z0), mark(z1)), false), 0, s(diff(p(leq(z0, z1)), false))), A__LEQ(mark(leq(z0, z1)), mark(false)), MARK(leq(z0, z1)))
   A__DIFF(if(z0, z1, z2), false) -> c11(A__IF(a__leq(a__if(mark(z0), z1, z2), false), 0, s(diff(p(if(z0, z1, z2)), false))), A__LEQ(mark(if(z0, z1, z2)), mark(false)), MARK(if(z0, z1, z2)))
   A__DIFF(diff(z0, z1), false) -> c11(A__IF(a__leq(a__diff(mark(z0), mark(z1)), false), 0, s(diff(p(diff(z0, z1)), false))), A__LEQ(mark(diff(z0, z1)), mark(false)), MARK(diff(z0, z1)))
   A__DIFF(s(z0), false) -> c11(A__IF(a__leq(s(mark(z0)), false), 0, s(diff(p(s(z0)), false))), A__LEQ(mark(s(z0)), mark(false)), MARK(s(z0)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)))
   A__DIFF(x0, false) -> c11(A__LEQ(mark(x0), mark(false)), MARK(x0))
   A__DIFF(0, false) -> c11(A__IF(a__leq(0, false), 0, s(diff(p(0), false))), A__LEQ(mark(0), mark(false)))
   A__DIFF(true, false) -> c11(A__IF(a__leq(true, false), 0, s(diff(p(true), false))), A__LEQ(mark(true), mark(false)))
   A__DIFF(false, false) -> c11(A__IF(a__leq(false, false), 0, s(diff(p(false), false))), A__LEQ(mark(false), mark(false)))
   A__DIFF(p(x0), x1) -> c11(A__IF(a__leq(p(mark(x0)), mark(x1)), 0, s(diff(p(p(x0)), x1))), A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(p(z0)), x1) -> c11(A__IF(a__leq(a__p(a__p(mark(z0))), mark(x1)), 0, s(diff(p(p(p(z0))), x1))), A__LEQ(mark(p(p(z0))), mark(x1)), MARK(p(p(z0))))
   A__DIFF(p(leq(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__leq(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(leq(z0, z1))), x1))), A__LEQ(mark(p(leq(z0, z1))), mark(x1)), MARK(p(leq(z0, z1))))
   A__DIFF(p(if(z0, z1, z2)), x1) -> c11(A__IF(a__leq(a__p(a__if(mark(z0), z1, z2)), mark(x1)), 0, s(diff(p(p(if(z0, z1, z2))), x1))), A__LEQ(mark(p(if(z0, z1, z2))), mark(x1)), MARK(p(if(z0, z1, z2))))
   A__DIFF(p(diff(z0, z1)), x1) -> c11(A__IF(a__leq(a__p(a__diff(mark(z0), mark(z1))), mark(x1)), 0, s(diff(p(p(diff(z0, z1))), x1))), A__LEQ(mark(p(diff(z0, z1))), mark(x1)), MARK(p(diff(z0, z1))))
   A__DIFF(p(s(z0)), x1) -> c11(A__IF(a__leq(a__p(s(mark(z0))), mark(x1)), 0, s(diff(p(p(s(z0))), x1))), A__LEQ(mark(p(s(z0))), mark(x1)), MARK(p(s(z0))))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)))
   A__DIFF(p(x0), x1) -> c11(A__LEQ(mark(p(x0)), mark(x1)), MARK(p(x0)))
   A__DIFF(p(0), x1) -> c11(A__IF(a__leq(a__p(0), mark(x1)), 0, s(diff(p(p(0)), x1))), A__LEQ(mark(p(0)), mark(x1)))
   A__DIFF(p(true), x1) -> c11(A__IF(a__leq(a__p(true), mark(x1)), 0, s(diff(p(p(true)), x1))), A__LEQ(mark(p(true)), mark(x1)))
   A__DIFF(p(false), x1) -> c11(A__IF(a__leq(a__p(false), mark(x1)), 0, s(diff(p(p(false)), x1))), A__LEQ(mark(p(false)), mark(x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__IF(a__leq(leq(mark(x0), mark(x1)), mark(x2)), 0, s(diff(p(leq(x0, x1)), x2))), A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(leq(x0, p(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__p(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, p(z0))), x2))), A__LEQ(mark(leq(x0, p(z0))), mark(x2)), MARK(leq(x0, p(z0))))
   A__DIFF(leq(x0, leq(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__leq(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, leq(z0, z1))), x2))), A__LEQ(mark(leq(x0, leq(z0, z1))), mark(x2)), MARK(leq(x0, leq(z0, z1))))
   A__DIFF(leq(x0, if(z0, z1, z2)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__if(mark(z0), z1, z2)), mark(x2)), 0, s(diff(p(leq(x0, if(z0, z1, z2))), x2))), A__LEQ(mark(leq(x0, if(z0, z1, z2))), mark(x2)), MARK(leq(x0, if(z0, z1, z2))))
   A__DIFF(leq(x0, diff(z0, z1)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), a__diff(mark(z0), mark(z1))), mark(x2)), 0, s(diff(p(leq(x0, diff(z0, z1))), x2))), A__LEQ(mark(leq(x0, diff(z0, z1))), mark(x2)), MARK(leq(x0, diff(z0, z1))))
   A__DIFF(leq(x0, 0), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), 0), mark(x2)), 0, s(diff(p(leq(x0, 0)), x2))), A__LEQ(mark(leq(x0, 0)), mark(x2)), MARK(leq(x0, 0)))
   A__DIFF(leq(x0, s(z0)), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), s(mark(z0))), mark(x2)), 0, s(diff(p(leq(x0, s(z0))), x2))), A__LEQ(mark(leq(x0, s(z0))), mark(x2)), MARK(leq(x0, s(z0))))
   A__DIFF(leq(x0, true), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), true), mark(x2)), 0, s(diff(p(leq(x0, true)), x2))), A__LEQ(mark(leq(x0, true)), mark(x2)), MARK(leq(x0, true)))
   A__DIFF(leq(x0, false), x2) -> c11(A__IF(a__leq(a__leq(mark(x0), false), mark(x2)), 0, s(diff(p(leq(x0, false)), x2))), A__LEQ(mark(leq(x0, false)), mark(x2)), MARK(leq(x0, false)))
   A__DIFF(leq(p(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(a__p(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(p(z0), x1)), x2))), A__LEQ(mark(leq(p(z0), x1)), mark(x2)), MARK(leq(p(z0), x1)))
   A__DIFF(leq(leq(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__leq(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(leq(z0, z1), x1)), x2))), A__LEQ(mark(leq(leq(z0, z1), x1)), mark(x2)), MARK(leq(leq(z0, z1), x1)))
   A__DIFF(leq(if(z0, z1, z2), x1), x2) -> c11(A__IF(a__leq(a__leq(a__if(mark(z0), z1, z2), mark(x1)), mark(x2)), 0, s(diff(p(leq(if(z0, z1, z2), x1)), x2))), A__LEQ(mark(leq(if(z0, z1, z2), x1)), mark(x2)), MARK(leq(if(z0, z1, z2), x1)))
   A__DIFF(leq(diff(z0, z1), x1), x2) -> c11(A__IF(a__leq(a__leq(a__diff(mark(z0), mark(z1)), mark(x1)), mark(x2)), 0, s(diff(p(leq(diff(z0, z1), x1)), x2))), A__LEQ(mark(leq(diff(z0, z1), x1)), mark(x2)), MARK(leq(diff(z0, z1), x1)))
   A__DIFF(leq(0, x1), x2) -> c11(A__IF(a__leq(a__leq(0, mark(x1)), mark(x2)), 0, s(diff(p(leq(0, x1)), x2))), A__LEQ(mark(leq(0, x1)), mark(x2)), MARK(leq(0, x1)))
   A__DIFF(leq(s(z0), x1), x2) -> c11(A__IF(a__leq(a__leq(s(mark(z0)), mark(x1)), mark(x2)), 0, s(diff(p(leq(s(z0), x1)), x2))), A__LEQ(mark(leq(s(z0), x1)), mark(x2)), MARK(leq(s(z0), x1)))
   A__DIFF(leq(true, x1), x2) -> c11(A__IF(a__leq(a__leq(true, mark(x1)), mark(x2)), 0, s(diff(p(leq(true, x1)), x2))), A__LEQ(mark(leq(true, x1)), mark(x2)), MARK(leq(true, x1)))
   A__DIFF(leq(false, x1), x2) -> c11(A__IF(a__leq(a__leq(false, mark(x1)), mark(x2)), 0, s(diff(p(leq(false, x1)), x2))), A__LEQ(mark(leq(false, x1)), mark(x2)), MARK(leq(false, x1)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)))
   A__DIFF(leq(x0, x1), x2) -> c11(A__LEQ(mark(leq(x0, x1)), mark(x2)), MARK(leq(x0, x1)))
   A__DIFF(if(x0, z1, z2), x3) -> c11(A__IF(a__leq(if(mark(x0), z1, z2), mark(x3)), 0, s(diff(p(if(x0, z1, z2)), x3))), A__LEQ(mark(if(x0, z1, z2)), mark(x3)), MARK(if(x0, z1, z2)))
   A__DIFF(if(p(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__p(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(p(z0), x1, x2)), x3))), A__LEQ(mark(if(p(z0), x1, x2)), mark(x3)), MARK(if(p(z0), x1, x2)))
   A__DIFF(if(leq(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__leq(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(leq(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(leq(z0, z1), x1, x2)), mark(x3)), MARK(if(leq(z0, z1), x1, x2)))
   A__DIFF(if(if(z0, z1, z2), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__if(mark(z0), z1, z2), x1, x2), mark(x3)), 0, s(diff(p(if(if(z0, z1, z2), x1, x2)), x3))), A__LEQ(mark(if(if(z0, z1, z2), x1, x2)), mark(x3)), MARK(if(if(z0, z1, z2), x1, x2)))
   A__DIFF(if(diff(z0, z1), x1, x2), x3) -> c11(A__IF(a__leq(a__if(a__diff(mark(z0), mark(z1)), x1, x2), mark(x3)), 0, s(diff(p(if(diff(z0, z1), x1, x2)), x3))), A__LEQ(mark(if(diff(z0, z1), x1, x2)), mark(x3)), MARK(if(diff(z0, z1), x1, x2)))
   A__DIFF(if(s(z0), x1, x2), x3) -> c11(A__IF(a__leq(a__if(s(mark(z0)), x1, x2), mark(x3)), 0, s(diff(p(if(s(z0), x1, x2)), x3))), A__LEQ(mark(if(s(z0), x1, x2)), mark(x3)), MARK(if(s(z0), x1, x2)))
   A__DIFF(if(true, x1, x2), x3) -> c11(A__IF(a__leq(a__if(true, x1, x2), mark(x3)), 0, s(diff(p(if(true, x1, x2)), x3))), A__LEQ(mark(if(true, x1, x2)), mark(x3)), MARK(if(true, x1, x2)))
   A__DIFF(if(false, x1, x2), x3) -> c11(A__IF(a__leq(a__if(false, x1, x2), mark(x3)), 0, s(diff(p(if(false, x1, x2)), x3))), A__LEQ(mark(if(false, x1, x2)), mark(x3)), MARK(if(false, x1, x2)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)))
   A__DIFF(if(x0, x1, x2), x3) -> c11(A__LEQ(mark(if(x0, x1, x2)), mark(x3)), MARK(if(x0, x1, x2)))
   A__DIFF(if(0, x1, x2), x3) -> c11(A__IF(a__leq(a__if(0, x1, x2), mark(x3)), 0, s(diff(p(if(0, x1, x2)), x3))), A__LEQ(mark(if(0, x1, x2)), mark(x3)))
K tuples:none
Defined Rule Symbols:   a__p_1, a__leq_2, a__if_3, a__diff_2, mark_1

Defined Pair Symbols:   A__P_1, A__IF_3, MARK_1, A__LEQ_2, A__DIFF_2

Compound Symbols:   c1_1, c8_1, c9_1, c18_2, c19_2, c21_1, c5_1, c6_1, c11_3, c11_2, c12_3, c12_2, c14_2, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c5_2, c6_2, c11_1