KILLED
proof of input_eptMJRhIyA.trs
# AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished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), 6 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 0 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 1847 ms]
    (16) BEST
        (17) proven lower bound
            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
            (19) BOUNDS(n^1, INF)
        (20) typed CpxTrs
            (21) RewriteLemmaProof [FINISHED, 2725 ms]
            (22) BOUNDS(EXP, INF)
(23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(24) CdtProblem
    (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CdtProblem
    (29) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (32) CdtProblem
    (33) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 2 ms]
    (36) CdtProblem
    (37) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CpxRelTRS
        (39) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (40) CpxTRS
        (41) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CpxWeightedTrs
            (43) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (44) CpxWeightedTrs
            (45) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (46) CpxTypedWeightedTrs
            (47) CompletionProof [UPPER BOUND(ID), 0 ms]
            (48) CpxTypedWeightedCompleteTrs
                (49) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
                (50) CpxTypedWeightedCompleteTrs
                (51) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (52) CpxRNTS
                (53) InliningProof [UPPER BOUND(ID), 1754 ms]
                (54) CpxRNTS
                (55) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (56) CpxRNTS
                (57) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
                (58) CpxRNTS
                (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (60) CpxRNTS
                (61) IntTrsBoundProof [UPPER BOUND(ID), 119 ms]
                (62) CpxRNTS
                (63) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
                (64) CpxRNTS
                (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (66) CpxRNTS
                (67) IntTrsBoundProof [UPPER BOUND(ID), 80 ms]
                (68) CpxRNTS
                (69) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
                (71) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (72) CpxRNTS
                (73) IntTrsBoundProof [UPPER BOUND(ID), 273 ms]
                (74) CpxRNTS
                (75) IntTrsBoundProof [UPPER BOUND(ID), 53 ms]
                (76) CpxRNTS
                (77) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (78) CpxRNTS
                (79) IntTrsBoundProof [UPPER BOUND(ID), 90 ms]
                (80) CpxRNTS
                (81) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
                (82) CpxRNTS
                (83) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (84) CpxRNTS
                (85) IntTrsBoundProof [UPPER BOUND(ID), 328 ms]
                (86) CpxRNTS
                (87) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
                (88) CpxRNTS
                (89) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (90) CpxRNTS
                (91) IntTrsBoundProof [UPPER BOUND(ID), 610 ms]
                (92) CpxRNTS
                (93) IntTrsBoundProof [UPPER BOUND(ID), 30 ms]
                (94) CpxRNTS
                (95) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (96) CpxRNTS
                (97) IntTrsBoundProof [UPPER BOUND(ID), 2053 ms]
                (98) CpxRNTS
                (99) IntTrsBoundProof [UPPER BOUND(ID), 296 ms]
                (100) CpxRNTS
                (101) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
                (102) CpxRNTS
                (103) IntTrsBoundProof [UPPER BOUND(ID), 1043 ms]
                (104) CpxRNTS
                (105) IntTrsBoundProof [UPPER BOUND(ID), 413 ms]
                (106) CpxRNTS
            (107) CompletionProof [UPPER BOUND(ID), 0 ms]
            (108) CpxTypedWeightedCompleteTrs
                (109) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (110) CpxRNTS
    (111) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 138 ms]
    (112) CdtProblem
        (113) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (134) CdtProblem
        (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
        (142) CdtProblem
        (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (154) CdtProblem
        (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (158) CdtProblem
        (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (162) CdtProblem
        (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (166) CdtProblem
        (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (170) CdtProblem
        (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (174) CdtProblem
        (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (182) CdtProblem
        (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (184) CdtProblem
        (185) CdtRewritingProof [BOTH BOUNDS(ID, ID), 1 ms]
        (186) CdtProblem
        (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (190) CdtProblem
        (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (192) CdtProblem
        (193) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 6 ms]
        (194) CdtProblem
        (195) CdtRewritingProof [BOTH BOUNDS(ID, ID), 116 ms]
        (196) CdtProblem
        (197) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (198) CdtProblem
        (199) CdtRewritingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (200) CdtProblem
        (201) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (202) CdtProblem
        (203) CdtRewritingProof [BOTH BOUNDS(ID, ID), 60 ms]
        (204) CdtProblem
        (205) CdtRewritingProof [BOTH BOUNDS(ID, ID), 109 ms]
        (206) CdtProblem
        (207) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (208) CdtProblem
        (209) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 80 ms]
        (210) CdtProblem
        (211) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 72 ms]
        (212) CdtProblem
        (213) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 43 ms]
        (214) CdtProblem
(215) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(216) CpxWeightedTrs
    (217) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (218) CpxWeightedTrs
    (219) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (220) CpxTypedWeightedTrs
    (221) CompletionProof [UPPER BOUND(ID), 0 ms]
    (222) CpxTypedWeightedCompleteTrs
        (223) NarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
        (224) CpxTypedWeightedCompleteTrs
        (225) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (226) CpxRNTS
        (227) InliningProof [UPPER BOUND(ID), 743 ms]
        (228) CpxRNTS
        (229) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (230) CpxRNTS
        (231) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (232) CpxRNTS
        (233) ResultPropagationProof [UPPER BOUND(ID), 6 ms]
        (234) CpxRNTS
        (235) IntTrsBoundProof [UPPER BOUND(ID), 209 ms]
        (236) CpxRNTS
        (237) IntTrsBoundProof [UPPER BOUND(ID), 69 ms]
        (238) CpxRNTS
        (239) ResultPropagationProof [UPPER BOUND(ID), 5 ms]
        (240) CpxRNTS
        (241) IntTrsBoundProof [UPPER BOUND(ID), 171 ms]
        (242) CpxRNTS
        (243) IntTrsBoundProof [UPPER BOUND(ID), 43 ms]
        (244) CpxRNTS
        (245) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (246) CpxRNTS
        (247) IntTrsBoundProof [UPPER BOUND(ID), 181 ms]
        (248) CpxRNTS
        (249) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
        (250) CpxRNTS
        (251) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (252) CpxRNTS
        (253) IntTrsBoundProof [UPPER BOUND(ID), 636 ms]
        (254) CpxRNTS
        (255) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
        (256) CpxRNTS
        (257) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (258) CpxRNTS
        (259) IntTrsBoundProof [UPPER BOUND(ID), 3351 ms]
        (260) CpxRNTS
        (261) IntTrsBoundProof [UPPER BOUND(ID), 6628 ms]
        (262) CpxRNTS
    (263) CompletionProof [UPPER BOUND(ID), 0 ms]
    (264) CpxTypedWeightedCompleteTrs
        (265) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms]
        (266) CpxRNTS


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

(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:

   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(x))) -> p(h(g(x)))
   g(0) -> pair(s(0), s(0))
   g(s(x)) -> h(g(x))
   h(x) -> pair(+(p(x), q(x)), p(x))
   p(pair(x, y)) -> x
   q(pair(x, y)) -> y
   +(x, 0) -> x
   +(x, s(y)) -> s(+(x, y))
   f(s(s(x))) -> +(p(g(x)), q(g(x)))
   g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))

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

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

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


The TRS R consists of the following rules:

   f(0') -> 0'
   f(s(0')) -> s(0')
   f(s(s(x))) -> p(h(g(x)))
   g(0') -> pair(s(0'), s(0'))
   g(s(x)) -> h(g(x))
   h(x) -> pair(+'(p(x), q(x)), p(x))
   p(pair(x, y)) -> x
   q(pair(x, y)) -> y
   +'(x, 0') -> x
   +'(x, s(y)) -> s(+'(x, y))
   f(s(s(x))) -> +'(p(g(x)), q(g(x)))
   g(s(x)) -> pair(+'(p(g(x)), q(g(x))), p(g(x)))

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

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

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


The TRS R consists of the following rules:

   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(x))) -> p(h(g(x)))
   g(0) -> pair(s(0), s(0))
   g(s(x)) -> h(g(x))
   h(x) -> pair(+(p(x), q(x)), p(x))
   p(pair(x, y)) -> x
   q(pair(x, y)) -> y
   +(x, 0) -> x
   +(x, s(y)) -> s(+(x, y))
   f(s(s(x))) -> +(p(g(x)), q(g(x)))
   g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x)))

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

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   F(0) -> c
   F(s(0)) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0) -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0) -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))
S tuples:
   F(0) -> c
   F(s(0)) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0) -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0) -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   F_1, G_1, H_1, P_1, Q_1, +'_2

Compound Symbols:   c, c1, c2_3, c3_3, c4_3, c5, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c12_1, c13, c14, c15, c16_1


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

(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(EXP, INF).


The TRS R consists of the following rules:

   F(0) -> c
   F(s(0)) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0) -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0) -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))

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

   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))

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(EXP, INF).


The TRS R consists of the following rules:

   F(0') -> c
   F(s(0')) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0') -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0') -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))

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

   f(0') -> 0'
   f(s(0')) -> s(0')
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +'(p(g(z0)), q(g(z0)))
   g(0') -> pair(s(0'), s(0'))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+'(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+'(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +'(z0, 0') -> z0
   +'(z0, s(z1)) -> s(+'(z0, z1))

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

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

(12)
Obligation:
Innermost TRS:
Rules:
F(0') -> c
F(s(0')) -> c1
F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(0') -> c5
G(s(z0)) -> c6(H(g(z0)), G(z0))
G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(s(z0)) -> c9(P(g(z0)), G(z0))
H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
H(z0) -> c12(P(z0))
P(pair(z0, z1)) -> c13
Q(pair(z0, z1)) -> c14
+'(z0, 0') -> c15
+'(z0, s(z1)) -> c16(+'(z0, z1))
f(0') -> 0'
f(s(0')) -> s(0')
f(s(s(z0))) -> p(h(g(z0)))
f(s(s(z0))) -> +'(p(g(z0)), q(g(z0)))
g(0') -> pair(s(0'), s(0'))
g(s(z0)) -> h(g(z0))
g(s(z0)) -> pair(+'(p(g(z0)), q(g(z0))), p(g(z0)))
h(z0) -> pair(+'(p(z0), q(z0)), p(z0))
p(pair(z0, z1)) -> z0
q(pair(z0, z1)) -> z1
+'(z0, 0') -> z0
+'(z0, s(z1)) -> s(+'(z0, z1))

Types:
F :: 0':s:c15:c16 -> c:c1:c2:c3:c4
0' :: 0':s:c15:c16
c :: c:c1:c2:c3:c4
s :: 0':s:c15:c16 -> 0':s:c15:c16
c1 :: c:c1:c2:c3:c4
c2 :: c13 -> c10:c11:c12 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
P :: pair -> c13
h :: pair -> pair
g :: 0':s:c15:c16 -> pair
H :: pair -> c10:c11:c12
G :: 0':s:c15:c16 -> c5:c6:c7:c8:c9
c3 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
+' :: 0':s:c15:c16 -> 0':s:c15:c16 -> 0':s:c15:c16
p :: pair -> 0':s:c15:c16
q :: pair -> 0':s:c15:c16
c4 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
Q :: pair -> c14
c5 :: c5:c6:c7:c8:c9
c6 :: c10:c11:c12 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c7 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c8 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c9 :: c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c10 :: 0':s:c15:c16 -> c13 -> c10:c11:c12
c11 :: 0':s:c15:c16 -> c14 -> c10:c11:c12
c12 :: c13 -> c10:c11:c12
pair :: 0':s:c15:c16 -> 0':s:c15:c16 -> pair
c13 :: c13
c14 :: c14
c15 :: 0':s:c15:c16
c16 :: 0':s:c15:c16 -> 0':s:c15:c16
f :: 0':s:c15:c16 -> 0':s:c15:c16
hole_c:c1:c2:c3:c41_17 :: c:c1:c2:c3:c4
hole_0':s:c15:c162_17 :: 0':s:c15:c16
hole_c133_17 :: c13
hole_c10:c11:c124_17 :: c10:c11:c12
hole_c5:c6:c7:c8:c95_17 :: c5:c6:c7:c8:c9
hole_pair6_17 :: pair
hole_c147_17 :: c14
gen_0':s:c15:c168_17 :: Nat -> 0':s:c15:c16
gen_c5:c6:c7:c8:c99_17 :: Nat -> c5:c6:c7:c8:c9

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
g, G, +'

They will be analysed ascendingly in the following order:
g < G
+' < g
+' < G

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

(14)
Obligation:
Innermost TRS:
Rules:
F(0') -> c
F(s(0')) -> c1
F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(0') -> c5
G(s(z0)) -> c6(H(g(z0)), G(z0))
G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(s(z0)) -> c9(P(g(z0)), G(z0))
H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
H(z0) -> c12(P(z0))
P(pair(z0, z1)) -> c13
Q(pair(z0, z1)) -> c14
+'(z0, 0') -> c15
+'(z0, s(z1)) -> c16(+'(z0, z1))
f(0') -> 0'
f(s(0')) -> s(0')
f(s(s(z0))) -> p(h(g(z0)))
f(s(s(z0))) -> +'(p(g(z0)), q(g(z0)))
g(0') -> pair(s(0'), s(0'))
g(s(z0)) -> h(g(z0))
g(s(z0)) -> pair(+'(p(g(z0)), q(g(z0))), p(g(z0)))
h(z0) -> pair(+'(p(z0), q(z0)), p(z0))
p(pair(z0, z1)) -> z0
q(pair(z0, z1)) -> z1
+'(z0, 0') -> z0
+'(z0, s(z1)) -> s(+'(z0, z1))

Types:
F :: 0':s:c15:c16 -> c:c1:c2:c3:c4
0' :: 0':s:c15:c16
c :: c:c1:c2:c3:c4
s :: 0':s:c15:c16 -> 0':s:c15:c16
c1 :: c:c1:c2:c3:c4
c2 :: c13 -> c10:c11:c12 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
P :: pair -> c13
h :: pair -> pair
g :: 0':s:c15:c16 -> pair
H :: pair -> c10:c11:c12
G :: 0':s:c15:c16 -> c5:c6:c7:c8:c9
c3 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
+' :: 0':s:c15:c16 -> 0':s:c15:c16 -> 0':s:c15:c16
p :: pair -> 0':s:c15:c16
q :: pair -> 0':s:c15:c16
c4 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
Q :: pair -> c14
c5 :: c5:c6:c7:c8:c9
c6 :: c10:c11:c12 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c7 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c8 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c9 :: c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c10 :: 0':s:c15:c16 -> c13 -> c10:c11:c12
c11 :: 0':s:c15:c16 -> c14 -> c10:c11:c12
c12 :: c13 -> c10:c11:c12
pair :: 0':s:c15:c16 -> 0':s:c15:c16 -> pair
c13 :: c13
c14 :: c14
c15 :: 0':s:c15:c16
c16 :: 0':s:c15:c16 -> 0':s:c15:c16
f :: 0':s:c15:c16 -> 0':s:c15:c16
hole_c:c1:c2:c3:c41_17 :: c:c1:c2:c3:c4
hole_0':s:c15:c162_17 :: 0':s:c15:c16
hole_c133_17 :: c13
hole_c10:c11:c124_17 :: c10:c11:c12
hole_c5:c6:c7:c8:c95_17 :: c5:c6:c7:c8:c9
hole_pair6_17 :: pair
hole_c147_17 :: c14
gen_0':s:c15:c168_17 :: Nat -> 0':s:c15:c16
gen_c5:c6:c7:c8:c99_17 :: Nat -> c5:c6:c7:c8:c9


Generator Equations:
gen_0':s:c15:c168_17(0) <=> 0'
gen_0':s:c15:c168_17(+(x, 1)) <=> s(gen_0':s:c15:c168_17(x))
gen_c5:c6:c7:c8:c99_17(0) <=> c5
gen_c5:c6:c7:c8:c99_17(+(x, 1)) <=> c6(c10(0', c13), gen_c5:c6:c7:c8:c99_17(x))


The following defined symbols remain to be analysed:
+', g, G

They will be analysed ascendingly in the following order:
g < G
+' < g
+' < G

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
+'(gen_0':s:c15:c168_17(a), gen_0':s:c15:c168_17(+(1, n11_17))) -> *10_17, rt in Omega(n11_17)

Induction Base:
+'(gen_0':s:c15:c168_17(a), gen_0':s:c15:c168_17(+(1, 0)))

Induction Step:
+'(gen_0':s:c15:c168_17(a), gen_0':s:c15:c168_17(+(1, +(n11_17, 1)))) ->_R^Omega(1)
c16(+'(gen_0':s:c15:c168_17(a), gen_0':s:c15:c168_17(+(1, n11_17)))) ->_IH
c16(*10_17)

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

(16)
Complex Obligation (BEST)

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

(17)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
F(0') -> c
F(s(0')) -> c1
F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(0') -> c5
G(s(z0)) -> c6(H(g(z0)), G(z0))
G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(s(z0)) -> c9(P(g(z0)), G(z0))
H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
H(z0) -> c12(P(z0))
P(pair(z0, z1)) -> c13
Q(pair(z0, z1)) -> c14
+'(z0, 0') -> c15
+'(z0, s(z1)) -> c16(+'(z0, z1))
f(0') -> 0'
f(s(0')) -> s(0')
f(s(s(z0))) -> p(h(g(z0)))
f(s(s(z0))) -> +'(p(g(z0)), q(g(z0)))
g(0') -> pair(s(0'), s(0'))
g(s(z0)) -> h(g(z0))
g(s(z0)) -> pair(+'(p(g(z0)), q(g(z0))), p(g(z0)))
h(z0) -> pair(+'(p(z0), q(z0)), p(z0))
p(pair(z0, z1)) -> z0
q(pair(z0, z1)) -> z1
+'(z0, 0') -> z0
+'(z0, s(z1)) -> s(+'(z0, z1))

Types:
F :: 0':s:c15:c16 -> c:c1:c2:c3:c4
0' :: 0':s:c15:c16
c :: c:c1:c2:c3:c4
s :: 0':s:c15:c16 -> 0':s:c15:c16
c1 :: c:c1:c2:c3:c4
c2 :: c13 -> c10:c11:c12 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
P :: pair -> c13
h :: pair -> pair
g :: 0':s:c15:c16 -> pair
H :: pair -> c10:c11:c12
G :: 0':s:c15:c16 -> c5:c6:c7:c8:c9
c3 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
+' :: 0':s:c15:c16 -> 0':s:c15:c16 -> 0':s:c15:c16
p :: pair -> 0':s:c15:c16
q :: pair -> 0':s:c15:c16
c4 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
Q :: pair -> c14
c5 :: c5:c6:c7:c8:c9
c6 :: c10:c11:c12 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c7 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c8 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c9 :: c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c10 :: 0':s:c15:c16 -> c13 -> c10:c11:c12
c11 :: 0':s:c15:c16 -> c14 -> c10:c11:c12
c12 :: c13 -> c10:c11:c12
pair :: 0':s:c15:c16 -> 0':s:c15:c16 -> pair
c13 :: c13
c14 :: c14
c15 :: 0':s:c15:c16
c16 :: 0':s:c15:c16 -> 0':s:c15:c16
f :: 0':s:c15:c16 -> 0':s:c15:c16
hole_c:c1:c2:c3:c41_17 :: c:c1:c2:c3:c4
hole_0':s:c15:c162_17 :: 0':s:c15:c16
hole_c133_17 :: c13
hole_c10:c11:c124_17 :: c10:c11:c12
hole_c5:c6:c7:c8:c95_17 :: c5:c6:c7:c8:c9
hole_pair6_17 :: pair
hole_c147_17 :: c14
gen_0':s:c15:c168_17 :: Nat -> 0':s:c15:c16
gen_c5:c6:c7:c8:c99_17 :: Nat -> c5:c6:c7:c8:c9


Generator Equations:
gen_0':s:c15:c168_17(0) <=> 0'
gen_0':s:c15:c168_17(+(x, 1)) <=> s(gen_0':s:c15:c168_17(x))
gen_c5:c6:c7:c8:c99_17(0) <=> c5
gen_c5:c6:c7:c8:c99_17(+(x, 1)) <=> c6(c10(0', c13), gen_c5:c6:c7:c8:c99_17(x))


The following defined symbols remain to be analysed:
+', g, G

They will be analysed ascendingly in the following order:
g < G
+' < g
+' < G

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

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

(19)
BOUNDS(n^1, INF)

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

(20)
Obligation:
Innermost TRS:
Rules:
F(0') -> c
F(s(0')) -> c1
F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(0') -> c5
G(s(z0)) -> c6(H(g(z0)), G(z0))
G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
G(s(z0)) -> c9(P(g(z0)), G(z0))
H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
H(z0) -> c12(P(z0))
P(pair(z0, z1)) -> c13
Q(pair(z0, z1)) -> c14
+'(z0, 0') -> c15
+'(z0, s(z1)) -> c16(+'(z0, z1))
f(0') -> 0'
f(s(0')) -> s(0')
f(s(s(z0))) -> p(h(g(z0)))
f(s(s(z0))) -> +'(p(g(z0)), q(g(z0)))
g(0') -> pair(s(0'), s(0'))
g(s(z0)) -> h(g(z0))
g(s(z0)) -> pair(+'(p(g(z0)), q(g(z0))), p(g(z0)))
h(z0) -> pair(+'(p(z0), q(z0)), p(z0))
p(pair(z0, z1)) -> z0
q(pair(z0, z1)) -> z1
+'(z0, 0') -> z0
+'(z0, s(z1)) -> s(+'(z0, z1))

Types:
F :: 0':s:c15:c16 -> c:c1:c2:c3:c4
0' :: 0':s:c15:c16
c :: c:c1:c2:c3:c4
s :: 0':s:c15:c16 -> 0':s:c15:c16
c1 :: c:c1:c2:c3:c4
c2 :: c13 -> c10:c11:c12 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
P :: pair -> c13
h :: pair -> pair
g :: 0':s:c15:c16 -> pair
H :: pair -> c10:c11:c12
G :: 0':s:c15:c16 -> c5:c6:c7:c8:c9
c3 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
+' :: 0':s:c15:c16 -> 0':s:c15:c16 -> 0':s:c15:c16
p :: pair -> 0':s:c15:c16
q :: pair -> 0':s:c15:c16
c4 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4
Q :: pair -> c14
c5 :: c5:c6:c7:c8:c9
c6 :: c10:c11:c12 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c7 :: 0':s:c15:c16 -> c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c8 :: 0':s:c15:c16 -> c14 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c9 :: c13 -> c5:c6:c7:c8:c9 -> c5:c6:c7:c8:c9
c10 :: 0':s:c15:c16 -> c13 -> c10:c11:c12
c11 :: 0':s:c15:c16 -> c14 -> c10:c11:c12
c12 :: c13 -> c10:c11:c12
pair :: 0':s:c15:c16 -> 0':s:c15:c16 -> pair
c13 :: c13
c14 :: c14
c15 :: 0':s:c15:c16
c16 :: 0':s:c15:c16 -> 0':s:c15:c16
f :: 0':s:c15:c16 -> 0':s:c15:c16
hole_c:c1:c2:c3:c41_17 :: c:c1:c2:c3:c4
hole_0':s:c15:c162_17 :: 0':s:c15:c16
hole_c133_17 :: c13
hole_c10:c11:c124_17 :: c10:c11:c12
hole_c5:c6:c7:c8:c95_17 :: c5:c6:c7:c8:c9
hole_pair6_17 :: pair
hole_c147_17 :: c14
gen_0':s:c15:c168_17 :: Nat -> 0':s:c15:c16
gen_c5:c6:c7:c8:c99_17 :: Nat -> c5:c6:c7:c8:c9


Lemmas:
+'(gen_0':s:c15:c168_17(a), gen_0':s:c15:c168_17(+(1, n11_17))) -> *10_17, rt in Omega(n11_17)


Generator Equations:
gen_0':s:c15:c168_17(0) <=> 0'
gen_0':s:c15:c168_17(+(x, 1)) <=> s(gen_0':s:c15:c168_17(x))
gen_c5:c6:c7:c8:c99_17(0) <=> c5
gen_c5:c6:c7:c8:c99_17(+(x, 1)) <=> c6(c10(0', c13), gen_c5:c6:c7:c8:c99_17(x))


The following defined symbols remain to be analysed:
g, G

They will be analysed ascendingly in the following order:
g < G

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

(21) RewriteLemmaProof (FINISHED)
Proved the following rewrite lemma:
g(gen_0':s:c15:c168_17(+(1, n2395_17))) -> *10_17, rt in Omega(EXP)

Induction Base:
g(gen_0':s:c15:c168_17(+(1, 0)))

Induction Step:
g(gen_0':s:c15:c168_17(+(1, +(n2395_17, 1)))) ->_R^Omega(0)
pair(+'(p(g(gen_0':s:c15:c168_17(+(1, n2395_17)))), q(g(gen_0':s:c15:c168_17(+(1, n2395_17))))), p(g(gen_0':s:c15:c168_17(+(1, n2395_17))))) ->_IH
pair(+'(p(*10_17), q(g(gen_0':s:c15:c168_17(+(1, n2395_17))))), p(g(gen_0':s:c15:c168_17(+(1, n2395_17))))) ->_IH
pair(+'(p(*10_17), q(*10_17)), p(g(gen_0':s:c15:c168_17(+(1, n2395_17))))) ->_IH
pair(+'(p(*10_17), q(*10_17)), p(*10_17))

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

(22)
BOUNDS(EXP, INF)

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

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

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   F(0) -> c
   F(s(0)) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0) -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0) -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))
S tuples:
   F(0) -> c
   F(s(0)) -> c1
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(0) -> c5
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   Q(pair(z0, z1)) -> c14
   +'(z0, 0) -> c15
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   F_1, G_1, H_1, P_1, Q_1, +'_2

Compound Symbols:   c, c1, c2_3, c3_3, c4_3, c5, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c12_1, c13, c14, c15, c16_1


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

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   F(0) -> c
   G(0) -> c5
   +'(z0, 0) -> c15
   Q(pair(z0, z1)) -> c14
   H(z0) -> c12(P(z0))
   P(pair(z0, z1)) -> c13
   F(s(0)) -> c1

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
S tuples:
   F(s(s(z0))) -> c2(P(h(g(z0))), H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), P(g(z0)), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), Q(g(z0)), G(z0))
   G(s(z0)) -> c9(P(g(z0)), G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)), P(z0))
   H(z0) -> c11(+'(p(z0), q(z0)), Q(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   F_1, G_1, H_1, +'_2

Compound Symbols:   c2_3, c3_3, c4_3, c6_2, c7_3, c8_3, c9_2, c10_2, c11_2, c16_1


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

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   F(s(s(z0))) -> c2(H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
S tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   F(s(s(z0))) -> c2(H(g(z0)), G(z0))
   F(s(s(z0))) -> c3(+'(p(g(z0)), q(g(z0))), G(z0))
   F(s(s(z0))) -> c4(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   G_1, +'_2, F_1, H_1

Compound Symbols:   c6_2, c16_1, c2_2, c3_2, c4_2, c7_2, c8_2, c9_1, c10_1, c11_1


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

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(G(z0))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(G(z0))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

(31) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   F(s(s(z0))) -> c(G(z0))

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
K tuples:none
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

(33) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
Defined Rule Symbols:   f_1, g_1, h_1, p_1, q_1, +_2

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

(35) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   f(0) -> 0
   f(s(0)) -> s(0)
   f(s(s(z0))) -> p(h(g(z0)))
   f(s(s(z0))) -> +(p(g(z0)), q(g(z0)))

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

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

(38)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))

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

   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1

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

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

(40)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1

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

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

(42)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(z0) -> c10(+'(p(z0), q(z0))) [1]
   H(z0) -> c11(+'(p(z0), q(z0))) [1]
   F(s(s(z0))) -> c(H(g(z0))) [0]
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(z0)) -> h(g(z0)) [0]
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(z0) -> pair(+(p(z0), q(z0)), p(z0)) [0]
   +(z0, 0) -> z0 [0]
   +(z0, s(z1)) -> s(+(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]

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

(43) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

+ => plus

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

(44)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(z0) -> c10(+'(p(z0), q(z0))) [1]
   H(z0) -> c11(+'(p(z0), q(z0))) [1]
   F(s(s(z0))) -> c(H(g(z0))) [0]
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(z0)) -> h(g(z0)) [0]
   g(s(z0)) -> pair(plus(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(z0) -> pair(plus(p(z0), q(z0)), p(z0)) [0]
   plus(z0, 0) -> z0 [0]
   plus(z0, s(z1)) -> s(plus(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]

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

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

(46)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   G(s(z0)) -> c6(H(g(z0)), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(z0) -> c10(+'(p(z0), q(z0))) [1]
   H(z0) -> c11(+'(p(z0), q(z0))) [1]
   F(s(s(z0))) -> c(H(g(z0))) [0]
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(z0)) -> h(g(z0)) [0]
   g(s(z0)) -> pair(plus(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(z0) -> pair(plus(p(z0), q(z0)), p(z0)) [0]
   plus(z0, 0) -> z0 [0]
   plus(z0, s(z1)) -> s(plus(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]

The TRS has the following type information:
G :: s:0 -> c6:c7:c8:c9
s :: s:0 -> s:0
c6 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
H :: pair -> c16:c10:c11
g :: s:0 -> pair
+' :: s:0 -> s:0 -> c16:c10:c11
c16 :: c16:c10:c11 -> c16:c10:c11
c7 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
p :: pair -> s:0
q :: pair -> s:0
c8 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
c9 :: c6:c7:c8:c9 -> c6:c7:c8:c9
c10 :: c16:c10:c11 -> c16:c10:c11
c11 :: c16:c10:c11 -> c16:c10:c11
F :: s:0 -> c
c :: c16:c10:c11 -> c
0 :: s:0
pair :: s:0 -> s:0 -> pair
h :: pair -> pair
plus :: s:0 -> s:0 -> s:0

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

(47) 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:

   G_1
   +'_2
   H_1

(c) The following functions are completely defined:

   F_1
   g_1
   h_1
   plus_2
   p_1
   q_1

Due to the following rules being added:

   F(v0) -> const3 [0]
   g(v0) -> const2 [0]
   h(v0) -> const2 [0]
   plus(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

And the following fresh constants:    const3, const2, const, const1

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

(48)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(z0) -> c10(+'(p(z0), q(z0))) [1]
   H(z0) -> c11(+'(p(z0), q(z0))) [1]
   F(s(s(z0))) -> c(H(g(z0))) [0]
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(z0)) -> h(g(z0)) [0]
   g(s(z0)) -> pair(plus(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(z0) -> pair(plus(p(z0), q(z0)), p(z0)) [0]
   plus(z0, 0) -> z0 [0]
   plus(z0, s(z1)) -> s(plus(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]
   F(v0) -> const3 [0]
   g(v0) -> const2 [0]
   h(v0) -> const2 [0]
   plus(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

The TRS has the following type information:
G :: s:0 -> c6:c7:c8:c9
s :: s:0 -> s:0
c6 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
H :: pair:const2 -> c16:c10:c11
g :: s:0 -> pair:const2
+' :: s:0 -> s:0 -> c16:c10:c11
c16 :: c16:c10:c11 -> c16:c10:c11
c7 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
p :: pair:const2 -> s:0
q :: pair:const2 -> s:0
c8 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
c9 :: c6:c7:c8:c9 -> c6:c7:c8:c9
c10 :: c16:c10:c11 -> c16:c10:c11
c11 :: c16:c10:c11 -> c16:c10:c11
F :: s:0 -> c:const3
c :: c16:c10:c11 -> c:const3
0 :: s:0
pair :: s:0 -> s:0 -> pair:const2
h :: pair:const2 -> pair:const2
plus :: s:0 -> s:0 -> s:0
const3 :: c:const3
const2 :: pair:const2
const :: c6:c7:c8:c9
const1 :: c16:c10:c11

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

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

(50)
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:

   G(s(0)) -> c6(H(pair(s(0), s(0))), G(0)) [1]
   G(s(s(z0'))) -> c6(H(h(g(z0'))), G(s(z0'))) [1]
   G(s(s(z0''))) -> c6(H(pair(plus(p(g(z0'')), q(g(z0''))), p(g(z0'')))), G(s(z0''))) [1]
   G(s(z0)) -> c6(H(const2), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), G(0)) [1]
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(const2)), G(0)) [1]
   G(s(s(z01))) -> c7(+'(p(h(g(z01))), q(h(g(z01)))), G(s(z01))) [1]
   G(s(s(z01))) -> c7(+'(p(h(g(z01))), q(pair(plus(p(g(z01)), q(g(z01))), p(g(z01))))), G(s(z01))) [1]
   G(s(s(z01))) -> c7(+'(p(h(g(z01))), q(const2)), G(s(z01))) [1]
   G(s(s(z02))) -> c7(+'(p(pair(plus(p(g(z02)), q(g(z02))), p(g(z02)))), q(h(g(z02)))), G(s(z02))) [1]
   G(s(s(z02))) -> c7(+'(p(pair(plus(p(g(z02)), q(g(z02))), p(g(z02)))), q(pair(plus(p(g(z02)), q(g(z02))), p(g(z02))))), G(s(z02))) [1]
   G(s(s(z02))) -> c7(+'(p(pair(plus(p(g(z02)), q(g(z02))), p(g(z02)))), q(const2)), G(s(z02))) [1]
   G(s(0)) -> c7(+'(p(const2), q(pair(s(0), s(0)))), G(0)) [1]
   G(s(s(z03))) -> c7(+'(p(const2), q(h(g(z03)))), G(s(z03))) [1]
   G(s(s(z04))) -> c7(+'(p(const2), q(pair(plus(p(g(z04)), q(g(z04))), p(g(z04))))), G(s(z04))) [1]
   G(s(z0)) -> c7(+'(p(const2), q(const2)), G(z0)) [1]
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), G(0)) [1]
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(const2)), G(0)) [1]
   G(s(s(z05))) -> c8(+'(p(h(g(z05))), q(h(g(z05)))), G(s(z05))) [1]
   G(s(s(z05))) -> c8(+'(p(h(g(z05))), q(pair(plus(p(g(z05)), q(g(z05))), p(g(z05))))), G(s(z05))) [1]
   G(s(s(z05))) -> c8(+'(p(h(g(z05))), q(const2)), G(s(z05))) [1]
   G(s(s(z06))) -> c8(+'(p(pair(plus(p(g(z06)), q(g(z06))), p(g(z06)))), q(h(g(z06)))), G(s(z06))) [1]
   G(s(s(z06))) -> c8(+'(p(pair(plus(p(g(z06)), q(g(z06))), p(g(z06)))), q(pair(plus(p(g(z06)), q(g(z06))), p(g(z06))))), G(s(z06))) [1]
   G(s(s(z06))) -> c8(+'(p(pair(plus(p(g(z06)), q(g(z06))), p(g(z06)))), q(const2)), G(s(z06))) [1]
   G(s(0)) -> c8(+'(p(const2), q(pair(s(0), s(0)))), G(0)) [1]
   G(s(s(z07))) -> c8(+'(p(const2), q(h(g(z07)))), G(s(z07))) [1]
   G(s(s(z08))) -> c8(+'(p(const2), q(pair(plus(p(g(z08)), q(g(z08))), p(g(z08))))), G(s(z08))) [1]
   G(s(z0)) -> c8(+'(p(const2), q(const2)), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(pair(z09, z1')) -> c10(+'(z09, z1')) [1]
   H(pair(z09, z1')) -> c10(+'(z09, 0)) [1]
   H(pair(z010, z1'')) -> c10(+'(0, z1'')) [1]
   H(z0) -> c10(+'(0, 0)) [1]
   H(pair(z011, z11)) -> c11(+'(z011, z11)) [1]
   H(pair(z011, z11)) -> c11(+'(z011, 0)) [1]
   H(pair(z012, z12)) -> c11(+'(0, z12)) [1]
   H(z0) -> c11(+'(0, 0)) [1]
   F(s(s(0))) -> c(H(pair(s(0), s(0)))) [0]
   F(s(s(s(z013)))) -> c(H(h(g(z013)))) [0]
   F(s(s(s(z014)))) -> c(H(pair(plus(p(g(z014)), q(g(z014))), p(g(z014))))) [0]
   F(s(s(z0))) -> c(H(const2)) [0]
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0))))) [0]
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(const2))) [0]
   F(s(s(s(z015)))) -> c(+'(p(h(g(z015))), q(h(g(z015))))) [0]
   F(s(s(s(z015)))) -> c(+'(p(h(g(z015))), q(pair(plus(p(g(z015)), q(g(z015))), p(g(z015)))))) [0]
   F(s(s(s(z015)))) -> c(+'(p(h(g(z015))), q(const2))) [0]
   F(s(s(s(z016)))) -> c(+'(p(pair(plus(p(g(z016)), q(g(z016))), p(g(z016)))), q(h(g(z016))))) [0]
   F(s(s(s(z016)))) -> c(+'(p(pair(plus(p(g(z016)), q(g(z016))), p(g(z016)))), q(pair(plus(p(g(z016)), q(g(z016))), p(g(z016)))))) [0]
   F(s(s(s(z016)))) -> c(+'(p(pair(plus(p(g(z016)), q(g(z016))), p(g(z016)))), q(const2))) [0]
   F(s(s(0))) -> c(+'(p(const2), q(pair(s(0), s(0))))) [0]
   F(s(s(s(z017)))) -> c(+'(p(const2), q(h(g(z017))))) [0]
   F(s(s(s(z018)))) -> c(+'(p(const2), q(pair(plus(p(g(z018)), q(g(z018))), p(g(z018)))))) [0]
   F(s(s(z0))) -> c(+'(p(const2), q(const2))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(0)) -> h(pair(s(0), s(0))) [0]
   g(s(s(z019))) -> h(h(g(z019))) [0]
   g(s(s(z020))) -> h(pair(plus(p(g(z020)), q(g(z020))), p(g(z020)))) [0]
   g(s(z0)) -> h(const2) [0]
   g(s(z0)) -> pair(plus(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(pair(z027, z13)) -> pair(plus(z027, z13), p(pair(z027, z13))) [0]
   h(pair(z027, z13)) -> pair(plus(z027, 0), p(pair(z027, z13))) [0]
   h(pair(z028, z14)) -> pair(plus(0, z14), p(pair(z028, z14))) [0]
   h(z0) -> pair(plus(0, 0), p(z0)) [0]
   plus(z0, 0) -> z0 [0]
   plus(z0, s(z1)) -> s(plus(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]
   F(v0) -> const3 [0]
   g(v0) -> const2 [0]
   h(v0) -> const2 [0]
   plus(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

The TRS has the following type information:
G :: s:0 -> c6:c7:c8:c9
s :: s:0 -> s:0
c6 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
H :: pair:const2 -> c16:c10:c11
g :: s:0 -> pair:const2
+' :: s:0 -> s:0 -> c16:c10:c11
c16 :: c16:c10:c11 -> c16:c10:c11
c7 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
p :: pair:const2 -> s:0
q :: pair:const2 -> s:0
c8 :: c16:c10:c11 -> c6:c7:c8:c9 -> c6:c7:c8:c9
c9 :: c6:c7:c8:c9 -> c6:c7:c8:c9
c10 :: c16:c10:c11 -> c16:c10:c11
c11 :: c16:c10:c11 -> c16:c10:c11
F :: s:0 -> c:const3
c :: c16:c10:c11 -> c:const3
0 :: s:0
pair :: s:0 -> s:0 -> pair:const2
h :: pair:const2 -> pair:const2
plus :: s:0 -> s:0 -> s:0
const3 :: c:const3
const2 :: pair:const2
const :: c6:c7:c8:c9
const1 :: c16:c10:c11

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

(51) 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
   const3 => 0
   const2 => 0
   const => 0
   const1 => 0

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

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ 1 }-> 1 + +'(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   F(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   F(z) -{ 0 }-> 1 + H(h(g(z013))) :|: z013 >= 0, z = 1 + (1 + (1 + z013))
   F(z) -{ 0 }-> 1 + H(0) :|: z0 >= 0, z = 1 + (1 + z0)
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z014)), q(g(z014))) + p(g(z014))) :|: z = 1 + (1 + (1 + z014)), z014 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), q(h(g(z015)))) :|: z015 >= 0, z = 1 + (1 + (1 + z015))
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), q(0)) :|: z015 >= 0, z = 1 + (1 + (1 + z015))
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), q(1 + plus(p(g(z015)), q(g(z015))) + p(g(z015)))) :|: z015 >= 0, z = 1 + (1 + (1 + z015))
   F(z) -{ 0 }-> 1 + +'(p(0), q(h(g(z017)))) :|: z = 1 + (1 + (1 + z017)), z017 >= 0
   F(z) -{ 0 }-> 1 + +'(p(0), q(0)) :|: z0 >= 0, z = 1 + (1 + z0)
   F(z) -{ 0 }-> 1 + +'(p(0), q(1 + plus(p(g(z018)), q(g(z018))) + p(g(z018)))) :|: z = 1 + (1 + (1 + z018)), z018 >= 0
   F(z) -{ 0 }-> 1 + +'(p(0), q(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), q(h(g(z016)))) :|: z = 1 + (1 + (1 + z016)), z016 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), q(0)) :|: z = 1 + (1 + (1 + z016)), z016 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), q(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016)))) :|: z = 1 + (1 + (1 + z016)), z016 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + (1 + 0) + (1 + 0)), q(0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(1 + (1 + 0) + (1 + 0)), q(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   G(z) -{ 1 }-> 1 + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z0'))) + G(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z0'')), q(g(z0''))) + p(g(z0''))) + G(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), q(h(g(z01)))) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), q(0)) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), q(1 + plus(p(g(z01)), q(g(z01))) + p(g(z01)))) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), q(h(g(z05)))) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05)
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), q(0)) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05)
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), q(1 + plus(p(g(z05)), q(g(z05))) + p(g(z05)))) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05)
   G(z) -{ 1 }-> 1 + +'(p(0), q(h(g(z03)))) + G(1 + z03) :|: z = 1 + (1 + z03), z03 >= 0
   G(z) -{ 1 }-> 1 + +'(p(0), q(h(g(z07)))) + G(1 + z07) :|: z = 1 + (1 + z07), z07 >= 0
   G(z) -{ 1 }-> 1 + +'(p(0), q(0)) + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + +'(p(0), q(1 + plus(p(g(z04)), q(g(z04))) + p(g(z04)))) + G(1 + z04) :|: z04 >= 0, z = 1 + (1 + z04)
   G(z) -{ 1 }-> 1 + +'(p(0), q(1 + plus(p(g(z08)), q(g(z08))) + p(g(z08)))) + G(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08)
   G(z) -{ 1 }-> 1 + +'(p(0), q(1 + (1 + 0) + (1 + 0))) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), q(h(g(z02)))) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), q(0)) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), q(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02)))) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), q(h(g(z06)))) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06)
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), q(0)) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06)
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), q(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06)))) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06)
   G(z) -{ 1 }-> 1 + +'(p(1 + (1 + 0) + (1 + 0)), q(0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(1 + (1 + 0) + (1 + 0)), q(1 + (1 + 0) + (1 + 0))) + G(0) :|: z = 1 + 0
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z = z0, z0 >= 0
   g(z) -{ 0 }-> h(h(g(z019))) :|: z019 >= 0, z = 1 + (1 + z019)
   g(z) -{ 0 }-> h(0) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z020)), q(g(z020))) + p(g(z020))) :|: z = 1 + (1 + z020), z020 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + plus(p(g(z0)), q(g(z0))) + p(g(z0)) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + p(1 + z027 + z13) :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + p(1 + z027 + z13) :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0
   h(z) -{ 0 }-> 1 + plus(0, z14) + p(1 + z028 + z14) :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0
   h(z) -{ 0 }-> 1 + plus(0, 0) + p(z0) :|: z = z0, z0 >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 0 }-> z0 :|: z = z0, z0 >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 0 }-> 1 + plus(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

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

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ 1 }-> 1 + +'(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   F(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   F(z) -{ 0 }-> 1 + H(h(g(z013))) :|: z013 >= 0, z = 1 + (1 + (1 + z013))
   F(z) -{ 0 }-> 1 + H(0) :|: z0 >= 0, z = 1 + (1 + z0)
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z014)), q(g(z014))) + p(g(z014))) :|: z = 1 + (1 + (1 + z014)), z014 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), q(h(g(z015)))) :|: z015 >= 0, z = 1 + (1 + (1 + z015))
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), q(1 + plus(p(g(z015)), q(g(z015))) + p(g(z015)))) :|: z015 >= 0, z = 1 + (1 + (1 + z015))
   F(z) -{ 0 }-> 1 + +'(p(h(g(z015))), 0) :|: z015 >= 0, z = 1 + (1 + (1 + z015)), v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), q(h(g(z016)))) :|: z = 1 + (1 + (1 + z016)), z016 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), q(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016)))) :|: z = 1 + (1 + (1 + z016)), z016 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z016)), q(g(z016))) + p(g(z016))), 0) :|: z = 1 + (1 + (1 + z016)), z016 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z017)))) :|: z = 1 + (1 + (1 + z017)), z017 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z018)), q(g(z018))) + p(g(z018)))) :|: z = 1 + (1 + (1 + z018)), z018 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z0 >= 0, z = 1 + (1 + z0), v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z0'))) + G(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z0'')), q(g(z0''))) + p(g(z0''))) + G(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), q(h(g(z01)))) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), q(1 + plus(p(g(z01)), q(g(z01))) + p(g(z01)))) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z01))), 0) + G(1 + z01) :|: z = 1 + (1 + z01), z01 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), q(h(g(z05)))) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05)
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), q(1 + plus(p(g(z05)), q(g(z05))) + p(g(z05)))) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05)
   G(z) -{ 1 }-> 1 + +'(p(h(g(z05))), 0) + G(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05), v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), q(h(g(z02)))) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), q(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02)))) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z02)), q(g(z02))) + p(g(z02))), 0) + G(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), q(h(g(z06)))) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06)
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), q(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06)))) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06)
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z06)), q(g(z06))) + p(g(z06))), 0) + G(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06), v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z03)))) + G(1 + z03) :|: z = 1 + (1 + z03), z03 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z07)))) + G(1 + z07) :|: z = 1 + (1 + z07), z07 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z04)), q(g(z04))) + p(g(z04)))) + G(1 + z04) :|: z04 >= 0, z = 1 + (1 + z04), v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z08)), q(g(z08))) + p(g(z08)))) + G(1 + z08) :|: z08 >= 0, z = 1 + (1 + z08), v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z0) :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z = z0, z0 >= 0
   g(z) -{ 0 }-> h(h(g(z019))) :|: z019 >= 0, z = 1 + (1 + z019)
   g(z) -{ 0 }-> h(0) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z020)), q(g(z020))) + p(g(z020))) :|: z = 1 + (1 + z020), z020 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + plus(p(g(z0)), q(g(z0))) + p(g(z0)) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z = z0, z0 >= 0, z1 >= 0, z0' >= 0, z0 = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z = z0, z0 >= 0, v0 >= 0, z0 = v0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 0 }-> z0 :|: z = z0, z0 >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 0 }-> 1 + plus(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ 1 }-> 1 + +'(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z - 1) :|: z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0


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(57) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { +' }
   { q }
   { plus }
   { p }
   { H }
   { h }
   { g }
   { F }
   { G }

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(58)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ 1 }-> 1 + +'(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z - 1) :|: z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {+'}, {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}

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

(59) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

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

   +'(z, z') -{ 1 }-> 1 + +'(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z - 1) :|: z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {+'}, {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: +'
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   +'(z, z') -{ 1 }-> 1 + +'(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z - 1) :|: z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {+'}, {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: ?, size: O(1) [0]

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: +'
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z'

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

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

   +'(z, z') -{ 1 }-> 1 + +'(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(z0, z1') :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + +'(z0, 0) :|: z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, z1) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + +'(0, 0) :|: z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(z0, z1') + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 }-> 1 + +'(z0, 0) + G(0) :|: z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, z1) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(0) :|: z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + +'(0, 0) + G(z - 1) :|: z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   H(z) -{ 1 }-> 1 + +'(z011, z11) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z011, 0) :|: z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, z1') :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(z09, 0) :|: z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + +'(0, z1'') :|: z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + +'(0, z12) :|: z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   H(z) -{ 1 }-> 1 + +'(0, 0) :|: z >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]

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

(65) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

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

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: q
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: ?, size: O(n^1) [z]

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: q
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

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

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]

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

(71) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(72)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

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

(74)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: ?, size: O(n^1) [z + z']

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

(75) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + plus(z027, z13) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, z13) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(z027, 0) + z0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(z027, 0) + 0 :|: z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + plus(0, z14) + z0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + plus(0, z14) + 0 :|: z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + plus(0, 0) + z0' :|: z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + plus(z, z' - 1) :|: z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']

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

(77) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']

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

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(80)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: ?, size: O(n^1) [z]

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

(81) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]

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

(83) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(84)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]

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

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: H
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(86)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {H}, {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: ?, size: O(1) [1]

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

(87) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: H
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

(88)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(0) :|: z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + (1 + 0) + (1 + 0)) :|: z = 1 + (1 + 0)
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(0) + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + (1 + 0) + (1 + 0)) + G(0) :|: z = 1 + 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]

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

(89) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(90)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]

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

(91) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: h
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 2*z

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

(92)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: ?, size: O(n^1) [1 + 2*z]

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

(93) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: h
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(94)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(0) :|: z - 1 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]

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

(95) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(96)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]

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

(97) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: g
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

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

(98)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  g: runtime: ?, size: EXP

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

(99) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(100)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 0 }-> 1 + H(h(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + H(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(h(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   F(z) -{ 0 }-> 1 + +'(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), 0) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(h(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + +'(0, q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + H(h(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + H(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(h(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0
   G(z) -{ 1 }-> 1 + +'(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), 0) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(h(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + +'(0, q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + G(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, 0 = v0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + plus(p(g(z - 1)), q(g(z - 1))) + p(g(z - 1)) :|: z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  g: runtime: O(1) [0], size: EXP

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

(101) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(102)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 2 + s134 + s136 }-> 1 + s137 :|: s130 >= 0, s130 <= inf28, s131 >= 0, s131 <= s130, s132 >= 0, s132 <= inf29, s133 >= 0, s133 <= s132, s134 >= 0, s134 <= s131 + s133, s135 >= 0, s135 <= inf30, s136 >= 0, s136 <= s135, s137 >= 0, s137 <= 1, z - 3 >= 0
   F(z) -{ s143 }-> 1 + s144 :|: s138 >= 0, s138 <= inf31, s139 >= 0, s139 <= 1 + 2 * s138, s140 >= 0, s140 <= s139, s141 >= 0, s141 <= inf32, s142 >= 0, s142 <= 1 + 2 * s141, s143 >= 0, s143 <= s142, s144 >= 0, s144 <= 0, z - 3 >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ s155 }-> 1 + s156 :|: s145 >= 0, s145 <= inf33, s146 >= 0, s146 <= 1 + 2 * s145, s147 >= 0, s147 <= s146, s148 >= 0, s148 <= inf34, s149 >= 0, s149 <= s148, s150 >= 0, s150 <= inf35, s151 >= 0, s151 <= s150, s152 >= 0, s152 <= s149 + s151, s153 >= 0, s153 <= inf36, s154 >= 0, s154 <= s153, s155 >= 0, s155 <= 1 + s152 + s154, s156 >= 0, s156 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + s160 :|: s157 >= 0, s157 <= inf37, s158 >= 0, s158 <= 1 + 2 * s157, s159 >= 0, s159 <= s158, s160 >= 0, s160 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s171 }-> 1 + s172 :|: s161 >= 0, s161 <= inf38, s162 >= 0, s162 <= s161, s163 >= 0, s163 <= inf39, s164 >= 0, s164 <= s163, s165 >= 0, s165 <= s162 + s164, s166 >= 0, s166 <= inf40, s167 >= 0, s167 <= s166, s168 >= 0, s168 <= 1 + s165 + s167, s169 >= 0, s169 <= inf41, s170 >= 0, s170 <= 1 + 2 * s169, s171 >= 0, s171 <= s170, s172 >= 0, s172 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ s188 }-> 1 + s189 :|: s173 >= 0, s173 <= inf42, s174 >= 0, s174 <= s173, s175 >= 0, s175 <= inf43, s176 >= 0, s176 <= s175, s177 >= 0, s177 <= s174 + s176, s178 >= 0, s178 <= inf44, s179 >= 0, s179 <= s178, s180 >= 0, s180 <= 1 + s177 + s179, s181 >= 0, s181 <= inf45, s182 >= 0, s182 <= s181, s183 >= 0, s183 <= inf46, s184 >= 0, s184 <= s183, s185 >= 0, s185 <= s182 + s184, s186 >= 0, s186 <= inf47, s187 >= 0, s187 <= s186, s188 >= 0, s188 <= 1 + s185 + s187, s189 >= 0, s189 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s198 :|: s190 >= 0, s190 <= inf48, s191 >= 0, s191 <= s190, s192 >= 0, s192 <= inf49, s193 >= 0, s193 <= s192, s194 >= 0, s194 <= s191 + s193, s195 >= 0, s195 <= inf50, s196 >= 0, s196 <= s195, s197 >= 0, s197 <= 1 + s194 + s196, s198 >= 0, s198 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ s201 }-> 1 + s202 :|: s199 >= 0, s199 <= inf51, s200 >= 0, s200 <= 1 + 2 * s199, s201 >= 0, s201 <= s200, s202 >= 0, s202 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s210 }-> 1 + s211 :|: s203 >= 0, s203 <= inf52, s204 >= 0, s204 <= s203, s205 >= 0, s205 <= inf53, s206 >= 0, s206 <= s205, s207 >= 0, s207 <= s204 + s206, s208 >= 0, s208 <= inf54, s209 >= 0, s209 <= s208, s210 >= 0, s210 <= 1 + s207 + s209, s211 >= 0, s211 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 1 + s43 }-> 1 + s44 :|: s42 >= 0, s42 <= inf', s43 >= 0, s43 <= 1 + 2 * s42, s44 >= 0, s44 <= 1, z - 3 >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 + s106 }-> 1 + s107 + G(1 + (z - 2)) :|: s91 >= 0, s91 <= inf15, s92 >= 0, s92 <= s91, s93 >= 0, s93 <= inf16, s94 >= 0, s94 <= s93, s95 >= 0, s95 <= s92 + s94, s96 >= 0, s96 <= inf17, s97 >= 0, s97 <= s96, s98 >= 0, s98 <= 1 + s95 + s97, s99 >= 0, s99 <= inf18, s100 >= 0, s100 <= s99, s101 >= 0, s101 <= inf19, s102 >= 0, s102 <= s101, s103 >= 0, s103 <= s100 + s102, s104 >= 0, s104 <= inf20, s105 >= 0, s105 <= s104, s106 >= 0, s106 <= 1 + s103 + s105, s107 >= 0, s107 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + s116 + G(1 + (z - 2)) :|: s108 >= 0, s108 <= inf21, s109 >= 0, s109 <= s108, s110 >= 0, s110 <= inf22, s111 >= 0, s111 <= s110, s112 >= 0, s112 <= s109 + s111, s113 >= 0, s113 <= inf23, s114 >= 0, s114 <= s113, s115 >= 0, s115 <= 1 + s112 + s114, s116 >= 0, s116 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 + s119 }-> 1 + s120 + G(1 + (z - 2)) :|: s117 >= 0, s117 <= inf24, s118 >= 0, s118 <= 1 + 2 * s117, s119 >= 0, s119 <= s118, s120 >= 0, s120 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + s128 }-> 1 + s129 + G(1 + (z - 2)) :|: s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s121, s123 >= 0, s123 <= inf26, s124 >= 0, s124 <= s123, s125 >= 0, s125 <= s122 + s124, s126 >= 0, s126 <= inf27, s127 >= 0, s127 <= s126, s128 >= 0, s128 <= 1 + s125 + s127, s129 >= 0, s129 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 2 + s40 }-> 1 + s41 + G(1 + (z - 2)) :|: s39 >= 0, s39 <= inf, s40 >= 0, s40 <= 1 + 2 * s39, s41 >= 0, s41 <= 1, z - 2 >= 0
   G(z) -{ 3 + s52 + s54 }-> 1 + s55 + G(1 + (z - 2)) :|: s48 >= 0, s48 <= inf1, s49 >= 0, s49 <= s48, s50 >= 0, s50 <= inf2, s51 >= 0, s51 <= s50, s52 >= 0, s52 <= s49 + s51, s53 >= 0, s53 <= inf3, s54 >= 0, s54 <= s53, s55 >= 0, s55 <= 1, z - 2 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 + s61 }-> 1 + s62 + G(1 + (z - 2)) :|: s56 >= 0, s56 <= inf4, s57 >= 0, s57 <= 1 + 2 * s56, s58 >= 0, s58 <= s57, s59 >= 0, s59 <= inf5, s60 >= 0, s60 <= 1 + 2 * s59, s61 >= 0, s61 <= s60, s62 >= 0, s62 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + s73 }-> 1 + s74 + G(1 + (z - 2)) :|: s63 >= 0, s63 <= inf6, s64 >= 0, s64 <= 1 + 2 * s63, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= inf7, s67 >= 0, s67 <= s66, s68 >= 0, s68 <= inf8, s69 >= 0, s69 <= s68, s70 >= 0, s70 <= s67 + s69, s71 >= 0, s71 <= inf9, s72 >= 0, s72 <= s71, s73 >= 0, s73 <= 1 + s70 + s72, s74 >= 0, s74 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s78 + G(1 + (z - 2)) :|: s75 >= 0, s75 <= inf10, s76 >= 0, s76 <= 1 + 2 * s75, s77 >= 0, s77 <= s76, s78 >= 0, s78 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 + s89 }-> 1 + s90 + G(1 + (z - 2)) :|: s79 >= 0, s79 <= inf11, s80 >= 0, s80 <= s79, s81 >= 0, s81 <= inf12, s82 >= 0, s82 <= s81, s83 >= 0, s83 <= s80 + s82, s84 >= 0, s84 <= inf13, s85 >= 0, s85 <= s84, s86 >= 0, s86 <= 1 + s83 + s85, s87 >= 0, s87 <= inf14, s88 >= 0, s88 <= 1 + 2 * s87, s89 >= 0, s89 <= s88, s90 >= 0, s90 <= 0, z - 2 >= 0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s219 :|: s212 >= 0, s212 <= inf55, s213 >= 0, s213 <= s212, s214 >= 0, s214 <= inf56, s215 >= 0, s215 <= s214, s216 >= 0, s216 <= s213 + s215, s217 >= 0, s217 <= inf57, s218 >= 0, s218 <= s217, s219 >= 0, s219 <= 1 + 2 * (1 + s216 + s218), z - 2 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> s47 :|: s45 >= 0, s45 <= inf'', s46 >= 0, s46 <= 1 + 2 * s45, s47 >= 0, s47 <= 1 + 2 * s46, z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + s224 + s226 :|: s220 >= 0, s220 <= inf58, s221 >= 0, s221 <= s220, s222 >= 0, s222 <= inf59, s223 >= 0, s223 <= s222, s224 >= 0, s224 <= s221 + s223, s225 >= 0, s225 <= inf60, s226 >= 0, s226 <= s225, z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  g: runtime: O(1) [0], size: EXP

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

(103) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

(104)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 2 + s134 + s136 }-> 1 + s137 :|: s130 >= 0, s130 <= inf28, s131 >= 0, s131 <= s130, s132 >= 0, s132 <= inf29, s133 >= 0, s133 <= s132, s134 >= 0, s134 <= s131 + s133, s135 >= 0, s135 <= inf30, s136 >= 0, s136 <= s135, s137 >= 0, s137 <= 1, z - 3 >= 0
   F(z) -{ s143 }-> 1 + s144 :|: s138 >= 0, s138 <= inf31, s139 >= 0, s139 <= 1 + 2 * s138, s140 >= 0, s140 <= s139, s141 >= 0, s141 <= inf32, s142 >= 0, s142 <= 1 + 2 * s141, s143 >= 0, s143 <= s142, s144 >= 0, s144 <= 0, z - 3 >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ s155 }-> 1 + s156 :|: s145 >= 0, s145 <= inf33, s146 >= 0, s146 <= 1 + 2 * s145, s147 >= 0, s147 <= s146, s148 >= 0, s148 <= inf34, s149 >= 0, s149 <= s148, s150 >= 0, s150 <= inf35, s151 >= 0, s151 <= s150, s152 >= 0, s152 <= s149 + s151, s153 >= 0, s153 <= inf36, s154 >= 0, s154 <= s153, s155 >= 0, s155 <= 1 + s152 + s154, s156 >= 0, s156 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + s160 :|: s157 >= 0, s157 <= inf37, s158 >= 0, s158 <= 1 + 2 * s157, s159 >= 0, s159 <= s158, s160 >= 0, s160 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s171 }-> 1 + s172 :|: s161 >= 0, s161 <= inf38, s162 >= 0, s162 <= s161, s163 >= 0, s163 <= inf39, s164 >= 0, s164 <= s163, s165 >= 0, s165 <= s162 + s164, s166 >= 0, s166 <= inf40, s167 >= 0, s167 <= s166, s168 >= 0, s168 <= 1 + s165 + s167, s169 >= 0, s169 <= inf41, s170 >= 0, s170 <= 1 + 2 * s169, s171 >= 0, s171 <= s170, s172 >= 0, s172 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ s188 }-> 1 + s189 :|: s173 >= 0, s173 <= inf42, s174 >= 0, s174 <= s173, s175 >= 0, s175 <= inf43, s176 >= 0, s176 <= s175, s177 >= 0, s177 <= s174 + s176, s178 >= 0, s178 <= inf44, s179 >= 0, s179 <= s178, s180 >= 0, s180 <= 1 + s177 + s179, s181 >= 0, s181 <= inf45, s182 >= 0, s182 <= s181, s183 >= 0, s183 <= inf46, s184 >= 0, s184 <= s183, s185 >= 0, s185 <= s182 + s184, s186 >= 0, s186 <= inf47, s187 >= 0, s187 <= s186, s188 >= 0, s188 <= 1 + s185 + s187, s189 >= 0, s189 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s198 :|: s190 >= 0, s190 <= inf48, s191 >= 0, s191 <= s190, s192 >= 0, s192 <= inf49, s193 >= 0, s193 <= s192, s194 >= 0, s194 <= s191 + s193, s195 >= 0, s195 <= inf50, s196 >= 0, s196 <= s195, s197 >= 0, s197 <= 1 + s194 + s196, s198 >= 0, s198 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ s201 }-> 1 + s202 :|: s199 >= 0, s199 <= inf51, s200 >= 0, s200 <= 1 + 2 * s199, s201 >= 0, s201 <= s200, s202 >= 0, s202 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s210 }-> 1 + s211 :|: s203 >= 0, s203 <= inf52, s204 >= 0, s204 <= s203, s205 >= 0, s205 <= inf53, s206 >= 0, s206 <= s205, s207 >= 0, s207 <= s204 + s206, s208 >= 0, s208 <= inf54, s209 >= 0, s209 <= s208, s210 >= 0, s210 <= 1 + s207 + s209, s211 >= 0, s211 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 1 + s43 }-> 1 + s44 :|: s42 >= 0, s42 <= inf', s43 >= 0, s43 <= 1 + 2 * s42, s44 >= 0, s44 <= 1, z - 3 >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 + s106 }-> 1 + s107 + G(1 + (z - 2)) :|: s91 >= 0, s91 <= inf15, s92 >= 0, s92 <= s91, s93 >= 0, s93 <= inf16, s94 >= 0, s94 <= s93, s95 >= 0, s95 <= s92 + s94, s96 >= 0, s96 <= inf17, s97 >= 0, s97 <= s96, s98 >= 0, s98 <= 1 + s95 + s97, s99 >= 0, s99 <= inf18, s100 >= 0, s100 <= s99, s101 >= 0, s101 <= inf19, s102 >= 0, s102 <= s101, s103 >= 0, s103 <= s100 + s102, s104 >= 0, s104 <= inf20, s105 >= 0, s105 <= s104, s106 >= 0, s106 <= 1 + s103 + s105, s107 >= 0, s107 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + s116 + G(1 + (z - 2)) :|: s108 >= 0, s108 <= inf21, s109 >= 0, s109 <= s108, s110 >= 0, s110 <= inf22, s111 >= 0, s111 <= s110, s112 >= 0, s112 <= s109 + s111, s113 >= 0, s113 <= inf23, s114 >= 0, s114 <= s113, s115 >= 0, s115 <= 1 + s112 + s114, s116 >= 0, s116 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 + s119 }-> 1 + s120 + G(1 + (z - 2)) :|: s117 >= 0, s117 <= inf24, s118 >= 0, s118 <= 1 + 2 * s117, s119 >= 0, s119 <= s118, s120 >= 0, s120 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + s128 }-> 1 + s129 + G(1 + (z - 2)) :|: s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s121, s123 >= 0, s123 <= inf26, s124 >= 0, s124 <= s123, s125 >= 0, s125 <= s122 + s124, s126 >= 0, s126 <= inf27, s127 >= 0, s127 <= s126, s128 >= 0, s128 <= 1 + s125 + s127, s129 >= 0, s129 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 2 + s40 }-> 1 + s41 + G(1 + (z - 2)) :|: s39 >= 0, s39 <= inf, s40 >= 0, s40 <= 1 + 2 * s39, s41 >= 0, s41 <= 1, z - 2 >= 0
   G(z) -{ 3 + s52 + s54 }-> 1 + s55 + G(1 + (z - 2)) :|: s48 >= 0, s48 <= inf1, s49 >= 0, s49 <= s48, s50 >= 0, s50 <= inf2, s51 >= 0, s51 <= s50, s52 >= 0, s52 <= s49 + s51, s53 >= 0, s53 <= inf3, s54 >= 0, s54 <= s53, s55 >= 0, s55 <= 1, z - 2 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 + s61 }-> 1 + s62 + G(1 + (z - 2)) :|: s56 >= 0, s56 <= inf4, s57 >= 0, s57 <= 1 + 2 * s56, s58 >= 0, s58 <= s57, s59 >= 0, s59 <= inf5, s60 >= 0, s60 <= 1 + 2 * s59, s61 >= 0, s61 <= s60, s62 >= 0, s62 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + s73 }-> 1 + s74 + G(1 + (z - 2)) :|: s63 >= 0, s63 <= inf6, s64 >= 0, s64 <= 1 + 2 * s63, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= inf7, s67 >= 0, s67 <= s66, s68 >= 0, s68 <= inf8, s69 >= 0, s69 <= s68, s70 >= 0, s70 <= s67 + s69, s71 >= 0, s71 <= inf9, s72 >= 0, s72 <= s71, s73 >= 0, s73 <= 1 + s70 + s72, s74 >= 0, s74 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s78 + G(1 + (z - 2)) :|: s75 >= 0, s75 <= inf10, s76 >= 0, s76 <= 1 + 2 * s75, s77 >= 0, s77 <= s76, s78 >= 0, s78 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 + s89 }-> 1 + s90 + G(1 + (z - 2)) :|: s79 >= 0, s79 <= inf11, s80 >= 0, s80 <= s79, s81 >= 0, s81 <= inf12, s82 >= 0, s82 <= s81, s83 >= 0, s83 <= s80 + s82, s84 >= 0, s84 <= inf13, s85 >= 0, s85 <= s84, s86 >= 0, s86 <= 1 + s83 + s85, s87 >= 0, s87 <= inf14, s88 >= 0, s88 <= 1 + 2 * s87, s89 >= 0, s89 <= s88, s90 >= 0, s90 <= 0, z - 2 >= 0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s219 :|: s212 >= 0, s212 <= inf55, s213 >= 0, s213 <= s212, s214 >= 0, s214 <= inf56, s215 >= 0, s215 <= s214, s216 >= 0, s216 <= s213 + s215, s217 >= 0, s217 <= inf57, s218 >= 0, s218 <= s217, s219 >= 0, s219 <= 1 + 2 * (1 + s216 + s218), z - 2 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> s47 :|: s45 >= 0, s45 <= inf'', s46 >= 0, s46 <= 1 + 2 * s45, s47 >= 0, s47 <= 1 + 2 * s46, z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + s224 + s226 :|: s220 >= 0, s220 <= inf58, s221 >= 0, s221 <= s220, s222 >= 0, s222 <= inf59, s223 >= 0, s223 <= s222, s224 >= 0, s224 <= s221 + s223, s225 >= 0, s225 <= inf60, s226 >= 0, s226 <= s225, z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  g: runtime: O(1) [0], size: EXP
  F: runtime: ?, size: O(1) [2]

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

(105) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(106)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z >= 0
   F(z) -{ 0 }-> 0 :|: z >= 0
   F(z) -{ 2 + s134 + s136 }-> 1 + s137 :|: s130 >= 0, s130 <= inf28, s131 >= 0, s131 <= s130, s132 >= 0, s132 <= inf29, s133 >= 0, s133 <= s132, s134 >= 0, s134 <= s131 + s133, s135 >= 0, s135 <= inf30, s136 >= 0, s136 <= s135, s137 >= 0, s137 <= 1, z - 3 >= 0
   F(z) -{ s143 }-> 1 + s144 :|: s138 >= 0, s138 <= inf31, s139 >= 0, s139 <= 1 + 2 * s138, s140 >= 0, s140 <= s139, s141 >= 0, s141 <= inf32, s142 >= 0, s142 <= 1 + 2 * s141, s143 >= 0, s143 <= s142, s144 >= 0, s144 <= 0, z - 3 >= 0
   F(z) -{ z1' }-> 1 + s15 :|: s15 >= 0, s15 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   F(z) -{ s155 }-> 1 + s156 :|: s145 >= 0, s145 <= inf33, s146 >= 0, s146 <= 1 + 2 * s145, s147 >= 0, s147 <= s146, s148 >= 0, s148 <= inf34, s149 >= 0, s149 <= s148, s150 >= 0, s150 <= inf35, s151 >= 0, s151 <= s150, s152 >= 0, s152 <= s149 + s151, s153 >= 0, s153 <= inf36, s154 >= 0, s154 <= s153, s155 >= 0, s155 <= 1 + s152 + s154, s156 >= 0, s156 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s16 :|: s16 >= 0, s16 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   F(z) -{ 0 }-> 1 + s160 :|: s157 >= 0, s157 <= inf37, s158 >= 0, s158 <= 1 + 2 * s157, s159 >= 0, s159 <= s158, s160 >= 0, s160 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s17 :|: s17 >= 0, s17 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s171 }-> 1 + s172 :|: s161 >= 0, s161 <= inf38, s162 >= 0, s162 <= s161, s163 >= 0, s163 <= inf39, s164 >= 0, s164 <= s163, s165 >= 0, s165 <= s162 + s164, s166 >= 0, s166 <= inf40, s167 >= 0, s167 <= s166, s168 >= 0, s168 <= 1 + s165 + s167, s169 >= 0, s169 <= inf41, s170 >= 0, s170 <= 1 + 2 * s169, s171 >= 0, s171 <= s170, s172 >= 0, s172 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s18 :|: s18 >= 0, s18 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ s188 }-> 1 + s189 :|: s173 >= 0, s173 <= inf42, s174 >= 0, s174 <= s173, s175 >= 0, s175 <= inf43, s176 >= 0, s176 <= s175, s177 >= 0, s177 <= s174 + s176, s178 >= 0, s178 <= inf44, s179 >= 0, s179 <= s178, s180 >= 0, s180 <= 1 + s177 + s179, s181 >= 0, s181 <= inf45, s182 >= 0, s182 <= s181, s183 >= 0, s183 <= inf46, s184 >= 0, s184 <= s183, s185 >= 0, s185 <= s182 + s184, s186 >= 0, s186 <= inf47, s187 >= 0, s187 <= s186, s188 >= 0, s188 <= 1 + s185 + s187, s189 >= 0, s189 <= 0, z - 3 >= 0
   F(z) -{ 0 }-> 1 + s19 :|: s19 >= 0, s19 <= 0, z = 1 + (1 + 0), z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s198 :|: s190 >= 0, s190 <= inf48, s191 >= 0, s191 <= s190, s192 >= 0, s192 <= inf49, s193 >= 0, s193 <= s192, s194 >= 0, s194 <= s191 + s193, s195 >= 0, s195 <= inf50, s196 >= 0, s196 <= s195, s197 >= 0, s197 <= 1 + s194 + s196, s198 >= 0, s198 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s20 :|: s20 >= 0, s20 <= 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   F(z) -{ s201 }-> 1 + s202 :|: s199 >= 0, s199 <= inf51, s200 >= 0, s200 <= 1 + 2 * s199, s201 >= 0, s201 <= s200, s202 >= 0, s202 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ z1 }-> 1 + s21 :|: s21 >= 0, s21 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   F(z) -{ s210 }-> 1 + s211 :|: s203 >= 0, s203 <= inf52, s204 >= 0, s204 <= s203, s205 >= 0, s205 <= inf53, s206 >= 0, s206 <= s205, s207 >= 0, s207 <= s204 + s206, s208 >= 0, s208 <= inf54, s209 >= 0, s209 <= s208, s210 >= 0, s210 <= 1 + s207 + s209, s211 >= 0, s211 <= 0, z - 3 >= 0, v0 >= 0, 0 = v0
   F(z) -{ 0 }-> 1 + s22 :|: s22 >= 0, s22 <= 0, z = 1 + (1 + 0), v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   F(z) -{ 0 }-> 1 + s23 :|: s23 >= 0, s23 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   F(z) -{ 4 }-> 1 + s35 :|: s35 >= 0, s35 <= 1, z = 1 + (1 + 0)
   F(z) -{ 1 }-> 1 + s36 :|: s36 >= 0, s36 <= 1, z - 2 >= 0
   F(z) -{ 1 + s43 }-> 1 + s44 :|: s42 >= 0, s42 <= inf', s43 >= 0, s43 <= 1 + 2 * s42, s44 >= 0, s44 <= 1, z - 3 >= 0
   G(z) -{ 1 }-> 1 + G(z - 1) :|: z - 1 >= 0
   G(z) -{ 1 }-> 1 + s10 + G(0) :|: s10 >= 0, s10 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 0 = v0
   G(z) -{ 1 + s106 }-> 1 + s107 + G(1 + (z - 2)) :|: s91 >= 0, s91 <= inf15, s92 >= 0, s92 <= s91, s93 >= 0, s93 <= inf16, s94 >= 0, s94 <= s93, s95 >= 0, s95 <= s92 + s94, s96 >= 0, s96 <= inf17, s97 >= 0, s97 <= s96, s98 >= 0, s98 <= 1 + s95 + s97, s99 >= 0, s99 <= inf18, s100 >= 0, s100 <= s99, s101 >= 0, s101 <= inf19, s102 >= 0, s102 <= s101, s103 >= 0, s103 <= s100 + s102, s104 >= 0, s104 <= inf20, s105 >= 0, s105 <= s104, s106 >= 0, s106 <= 1 + s103 + s105, s107 >= 0, s107 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s11 + G(0) :|: s11 >= 0, s11 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 0 = v0'
   G(z) -{ 1 }-> 1 + s116 + G(1 + (z - 2)) :|: s108 >= 0, s108 <= inf21, s109 >= 0, s109 <= s108, s110 >= 0, s110 <= inf22, s111 >= 0, s111 <= s110, s112 >= 0, s112 <= s109 + s111, s113 >= 0, s113 <= inf23, s114 >= 0, s114 <= s113, s115 >= 0, s115 <= 1 + s112 + s114, s116 >= 0, s116 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s12 + G(0) :|: s12 >= 0, s12 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 + s119 }-> 1 + s120 + G(1 + (z - 2)) :|: s117 >= 0, s117 <= inf24, s118 >= 0, s118 <= 1 + 2 * s117, s119 >= 0, s119 <= s118, s120 >= 0, s120 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + s128 }-> 1 + s129 + G(1 + (z - 2)) :|: s121 >= 0, s121 <= inf25, s122 >= 0, s122 <= s121, s123 >= 0, s123 <= inf26, s124 >= 0, s124 <= s123, s125 >= 0, s125 <= s122 + s124, s126 >= 0, s126 <= inf27, s127 >= 0, s127 <= s126, s128 >= 0, s128 <= 1 + s125 + s127, s129 >= 0, s129 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 }-> 1 + s13 + G(0) :|: s13 >= 0, s13 <= 0, z = 1 + 0, v0 >= 0, 0 = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 }-> 1 + s14 + G(z - 1) :|: s14 >= 0, s14 <= 0, z - 1 >= 0, v0 >= 0, 0 = v0, v0' >= 0, 0 = v0'
   G(z) -{ 5 }-> 1 + s33 + G(0) :|: s33 >= 0, s33 <= 1, z = 1 + 0
   G(z) -{ 2 }-> 1 + s34 + G(z - 1) :|: s34 >= 0, s34 <= 1, z - 1 >= 0
   G(z) -{ 2 + s40 }-> 1 + s41 + G(1 + (z - 2)) :|: s39 >= 0, s39 <= inf, s40 >= 0, s40 <= 1 + 2 * s39, s41 >= 0, s41 <= 1, z - 2 >= 0
   G(z) -{ 3 + s52 + s54 }-> 1 + s55 + G(1 + (z - 2)) :|: s48 >= 0, s48 <= inf1, s49 >= 0, s49 <= s48, s50 >= 0, s50 <= inf2, s51 >= 0, s51 <= s50, s52 >= 0, s52 <= s49 + s51, s53 >= 0, s53 <= inf3, s54 >= 0, s54 <= s53, s55 >= 0, s55 <= 1, z - 2 >= 0
   G(z) -{ 1 + z1' }-> 1 + s6 + G(0) :|: s6 >= 0, s6 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, z1' >= 0, z0' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0' + z1'
   G(z) -{ 1 + s61 }-> 1 + s62 + G(1 + (z - 2)) :|: s56 >= 0, s56 <= inf4, s57 >= 0, s57 <= 1 + 2 * s56, s58 >= 0, s58 <= s57, s59 >= 0, s59 <= inf5, s60 >= 0, s60 <= 1 + 2 * s59, s61 >= 0, s61 <= s60, s62 >= 0, s62 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s7 + G(0) :|: s7 >= 0, s7 <= 0, z = 1 + 0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   G(z) -{ 1 + s73 }-> 1 + s74 + G(1 + (z - 2)) :|: s63 >= 0, s63 <= inf6, s64 >= 0, s64 <= 1 + 2 * s63, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= inf7, s67 >= 0, s67 <= s66, s68 >= 0, s68 <= inf8, s69 >= 0, s69 <= s68, s70 >= 0, s70 <= s67 + s69, s71 >= 0, s71 <= inf9, s72 >= 0, s72 <= s71, s73 >= 0, s73 <= 1 + s70 + s72, s74 >= 0, s74 <= 0, z - 2 >= 0
   G(z) -{ 1 }-> 1 + s78 + G(1 + (z - 2)) :|: s75 >= 0, s75 <= inf10, s76 >= 0, s76 <= 1 + 2 * s75, s77 >= 0, s77 <= s76, s78 >= 0, s78 <= 0, z - 2 >= 0, v0 >= 0, 0 = v0
   G(z) -{ 1 + z1 }-> 1 + s8 + G(0) :|: s8 >= 0, s8 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, z1 >= 0, z0 >= 0, 1 + (1 + 0) + (1 + 0) = 1 + z0 + z1
   G(z) -{ 1 }-> 1 + s9 + G(0) :|: s9 >= 0, s9 <= 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   G(z) -{ 1 + s89 }-> 1 + s90 + G(1 + (z - 2)) :|: s79 >= 0, s79 <= inf11, s80 >= 0, s80 <= s79, s81 >= 0, s81 <= inf12, s82 >= 0, s82 <= s81, s83 >= 0, s83 <= s80 + s82, s84 >= 0, s84 <= inf13, s85 >= 0, s85 <= s84, s86 >= 0, s86 <= 1 + s83 + s85, s87 >= 0, s87 <= inf14, s88 >= 0, s88 <= 1 + 2 * s87, s89 >= 0, s89 <= s88, s90 >= 0, s90 <= 0, z - 2 >= 0
   H(z) -{ 1 + z1' }-> 1 + s' :|: s' >= 0, s' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 }-> 1 + s'' :|: s'' >= 0, s'' <= 0, z = 1 + z09 + z1', z1' >= 0, z09 >= 0
   H(z) -{ 1 + z1'' }-> 1 + s1 :|: s1 >= 0, s1 <= 0, z = 1 + z010 + z1'', z010 >= 0, z1'' >= 0
   H(z) -{ 1 }-> 1 + s2 :|: s2 >= 0, s2 <= 0, z >= 0
   H(z) -{ 1 + z11 }-> 1 + s3 :|: s3 >= 0, s3 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 }-> 1 + s4 :|: s4 >= 0, s4 <= 0, z = 1 + z011 + z11, z011 >= 0, z11 >= 0
   H(z) -{ 1 + z12 }-> 1 + s5 :|: s5 >= 0, s5 <= 0, z = 1 + z012 + z12, z012 >= 0, z12 >= 0
   g(z) -{ 0 }-> s219 :|: s212 >= 0, s212 <= inf55, s213 >= 0, s213 <= s212, s214 >= 0, s214 <= inf56, s215 >= 0, s215 <= s214, s216 >= 0, s216 <= s213 + s215, s217 >= 0, s217 <= inf57, s218 >= 0, s218 <= s217, s219 >= 0, s219 <= 1 + 2 * (1 + s216 + s218), z - 2 >= 0
   g(z) -{ 0 }-> s37 :|: s37 >= 0, s37 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 0 }-> s38 :|: s38 >= 0, s38 <= 1 + 2 * 0, z - 1 >= 0
   g(z) -{ 0 }-> s47 :|: s45 >= 0, s45 <= inf'', s46 >= 0, s46 <= 1 + 2 * s45, s47 >= 0, s47 <= 1 + 2 * s46, z - 2 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + s224 + s226 :|: s220 >= 0, s220 <= inf58, s221 >= 0, s221 <= s220, s222 >= 0, s222 <= inf59, s223 >= 0, s223 <= s222, s224 >= 0, s224 <= s221 + s223, s225 >= 0, s225 <= inf60, s226 >= 0, s226 <= s225, z - 1 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: z >= 0
   h(z) -{ 0 }-> 1 + s25 + z0 :|: s25 >= 0, s25 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s26 + 0 :|: s26 >= 0, s26 <= z027 + z13, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s27 + z0 :|: s27 >= 0, s27 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, z1 >= 0, z0 >= 0, 1 + z027 + z13 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s28 + 0 :|: s28 >= 0, s28 <= z027 + 0, z = 1 + z027 + z13, z027 >= 0, z13 >= 0, v0 >= 0, 1 + z027 + z13 = v0
   h(z) -{ 0 }-> 1 + s29 + z0 :|: s29 >= 0, s29 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, z1 >= 0, z0 >= 0, 1 + z028 + z14 = 1 + z0 + z1
   h(z) -{ 0 }-> 1 + s30 + 0 :|: s30 >= 0, s30 <= 0 + z14, z = 1 + z028 + z14, z028 >= 0, z14 >= 0, v0 >= 0, 1 + z028 + z14 = v0
   h(z) -{ 0 }-> 1 + s31 + z0' :|: s31 >= 0, s31 <= 0 + 0, z >= 0, z1 >= 0, z0' >= 0, z = 1 + z0' + z1
   h(z) -{ 0 }-> 1 + s32 + 0 :|: s32 >= 0, s32 <= 0 + 0, z >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 0 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   plus(z, z') -{ 0 }-> 1 + s24 :|: s24 >= 0, s24 <= z + (z' - 1), z' - 1 >= 0, z >= 0
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {F}, {G}
Previous analysis results are:
  +': runtime: O(n^1) [z'], size: O(1) [0]
  q: runtime: O(1) [0], size: O(n^1) [z]
  plus: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  H: runtime: O(n^1) [1 + z], size: O(1) [1]
  h: runtime: O(1) [0], size: O(n^1) [1 + 2*z]
  g: runtime: O(1) [0], size: EXP
  F: runtime: INF, size: O(1) [2]

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

(107) 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:

   F(v0) -> null_F [0]
   g(v0) -> null_g [0]
   h(v0) -> null_h [0]
   plus(v0, v1) -> null_plus [0]
   p(v0) -> null_p [0]
   q(v0) -> null_q [0]
   G(v0) -> null_G [0]
   +'(v0, v1) -> null_+' [0]

And the following fresh constants:    null_F, null_g, null_h, null_plus, null_p, null_q, null_G, null_+'

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

(108)
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:

   G(s(z0)) -> c6(H(g(z0)), G(z0)) [1]
   +'(z0, s(z1)) -> c16(+'(z0, z1)) [1]
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) [1]
   G(s(z0)) -> c9(G(z0)) [1]
   H(z0) -> c10(+'(p(z0), q(z0))) [1]
   H(z0) -> c11(+'(p(z0), q(z0))) [1]
   F(s(s(z0))) -> c(H(g(z0))) [0]
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) [0]
   g(0) -> pair(s(0), s(0)) [0]
   g(s(z0)) -> h(g(z0)) [0]
   g(s(z0)) -> pair(plus(p(g(z0)), q(g(z0))), p(g(z0))) [0]
   h(z0) -> pair(plus(p(z0), q(z0)), p(z0)) [0]
   plus(z0, 0) -> z0 [0]
   plus(z0, s(z1)) -> s(plus(z0, z1)) [0]
   p(pair(z0, z1)) -> z0 [0]
   q(pair(z0, z1)) -> z1 [0]
   F(v0) -> null_F [0]
   g(v0) -> null_g [0]
   h(v0) -> null_h [0]
   plus(v0, v1) -> null_plus [0]
   p(v0) -> null_p [0]
   q(v0) -> null_q [0]
   G(v0) -> null_G [0]
   +'(v0, v1) -> null_+' [0]

The TRS has the following type information:
G :: s:0:null_plus:null_p:null_q -> c6:c7:c8:c9:null_G
s :: s:0:null_plus:null_p:null_q -> s:0:null_plus:null_p:null_q
c6 :: c16:c10:c11:null_+' -> c6:c7:c8:c9:null_G -> c6:c7:c8:c9:null_G
H :: pair:null_g:null_h -> c16:c10:c11:null_+'
g :: s:0:null_plus:null_p:null_q -> pair:null_g:null_h
+' :: s:0:null_plus:null_p:null_q -> s:0:null_plus:null_p:null_q -> c16:c10:c11:null_+'
c16 :: c16:c10:c11:null_+' -> c16:c10:c11:null_+'
c7 :: c16:c10:c11:null_+' -> c6:c7:c8:c9:null_G -> c6:c7:c8:c9:null_G
p :: pair:null_g:null_h -> s:0:null_plus:null_p:null_q
q :: pair:null_g:null_h -> s:0:null_plus:null_p:null_q
c8 :: c16:c10:c11:null_+' -> c6:c7:c8:c9:null_G -> c6:c7:c8:c9:null_G
c9 :: c6:c7:c8:c9:null_G -> c6:c7:c8:c9:null_G
c10 :: c16:c10:c11:null_+' -> c16:c10:c11:null_+'
c11 :: c16:c10:c11:null_+' -> c16:c10:c11:null_+'
F :: s:0:null_plus:null_p:null_q -> c:null_F
c :: c16:c10:c11:null_+' -> c:null_F
0 :: s:0:null_plus:null_p:null_q
pair :: s:0:null_plus:null_p:null_q -> s:0:null_plus:null_p:null_q -> pair:null_g:null_h
h :: pair:null_g:null_h -> pair:null_g:null_h
plus :: s:0:null_plus:null_p:null_q -> s:0:null_plus:null_p:null_q -> s:0:null_plus:null_p:null_q
null_F :: c:null_F
null_g :: pair:null_g:null_h
null_h :: pair:null_g:null_h
null_plus :: s:0:null_plus:null_p:null_q
null_p :: s:0:null_plus:null_p:null_q
null_q :: s:0:null_plus:null_p:null_q
null_G :: c6:c7:c8:c9:null_G
null_+' :: c16:c10:c11:null_+'

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

(109) 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
   null_F => 0
   null_g => 0
   null_h => 0
   null_plus => 0
   null_p => 0
   null_q => 0
   null_G => 0
   null_+' => 0

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

(110)
Obligation:
Complexity RNTS consisting of the following rules:

   +'(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   +'(z, z') -{ 1 }-> 1 + +'(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   F(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   F(z) -{ 0 }-> 1 + H(g(z0)) :|: z0 >= 0, z = 1 + (1 + z0)
   F(z) -{ 0 }-> 1 + +'(p(g(z0)), q(g(z0))) :|: z0 >= 0, z = 1 + (1 + z0)
   G(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   G(z) -{ 1 }-> 1 + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + H(g(z0)) + G(z0) :|: z = 1 + z0, z0 >= 0
   G(z) -{ 1 }-> 1 + +'(p(g(z0)), q(g(z0))) + G(z0) :|: z = 1 + z0, z0 >= 0
   H(z) -{ 1 }-> 1 + +'(p(z0), q(z0)) :|: z = z0, z0 >= 0
   g(z) -{ 0 }-> h(g(z0)) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + plus(p(g(z0)), q(g(z0))) + p(g(z0)) :|: z = 1 + z0, z0 >= 0
   g(z) -{ 0 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   h(z) -{ 0 }-> 1 + plus(p(z0), q(z0)) + p(z0) :|: z = z0, z0 >= 0
   p(z) -{ 0 }-> z0 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 0 }-> z0 :|: z = z0, z0 >= 0, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 0 }-> 1 + plus(z0, z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   q(z) -{ 0 }-> z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

Only complete derivations are relevant for the runtime complexity.

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

(111) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
We considered the (Usable) Rules:none
And the Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(+(x_1, x_2)) = [1]
   POL(+'(x_1, x_2)) = 0
   POL(0) = [1]
   POL(F(x_1)) = [1] + x_1
   POL(G(x_1)) = x_1
   POL(H(x_1)) = 0
   POL(c(x_1)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c16(x_1)) = x_1
   POL(c6(x_1, x_2)) = x_1 + x_2
   POL(c7(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c9(x_1)) = x_1
   POL(g(x_1)) = x_1
   POL(h(x_1)) = [1] + x_1
   POL(p(x_1)) = [1]
   POL(pair(x_1, x_2)) = [1]
   POL(q(x_1)) = [1]
   POL(s(x_1)) = [1] + x_1

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

(113) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c7_2, c8_2, c9_1, c10_1, c11_1, c_1


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0)) by 
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))), G(0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))), G(0))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))), G(0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))), G(0))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c8_2, c9_1, c10_1, c11_1, c_1, c7_2


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c8_2, c9_1, c10_1, c11_1, c_1, c7_2, c7_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0)) by 
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))), G(0))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))), G(0))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))), G(0))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))), G(0))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c9_1, c10_1, c11_1, c_1, c7_2, c7_1, c8_2


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c9_1, c10_1, c11_1, c_1, c7_2, c7_1, c8_2, c8_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(z0) -> c10(+'(p(z0), q(z0))) by 
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c11(+'(p(z0), q(z0)))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, H_1, F_1

Compound Symbols:   c6_2, c16_1, c9_1, c11_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(z0) -> c11(+'(p(z0), q(z0))) by 
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, +'_2, F_1, H_1

Compound Symbols:   c6_2, c16_1, c9_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(z0)) -> c6(H(g(z0)), G(z0)) by 
   G(s(0)) -> c6(H(pair(s(0), s(0))), G(0))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(0)) -> c6(H(pair(s(0), s(0))), G(0))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2


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

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(z0))) -> c(H(g(z0))) by 
   F(s(s(0))) -> c(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(0))) -> c(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(H(g(z0)))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c6(H(g(z0)), G(z0))
   G(s(z0)) -> c7(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c8(+'(p(g(z0)), q(g(z0))), G(z0))
   G(s(z0)) -> c9(G(z0))
   H(z0) -> c10(+'(p(z0), q(z0)))
   H(z0) -> c11(+'(p(z0), q(z0)))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1


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

(133) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   F(s(s(0))) -> c(H(pair(s(0), s(0))))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0)))) by 
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0))) by 
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0))) by 
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0))) by 
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0))) by 
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(0)) -> c7(+'(p(g(0)), q(pair(s(0), s(0))))) by 
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0))))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(g(0)))) by 
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(h(g(z0)))), G(s(z0))) by 
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0))) by 
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(g(s(z0)))), G(s(z0))) by 
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0))) by 
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(0)) -> c8(+'(p(g(0)), q(pair(s(0), s(0))))) by 
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c8_1, c10_1, c11_1, c6_2, c6_1, c_1, c7_1


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(g(0)))) by 
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c10_1, c11_1, c6_2, c6_1, c_1, c7_1, c8_1


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(pair(z0, z1)) -> c10(+'(p(pair(z0, z1)), z1)) by 
   H(pair(z0, z1)) -> c10(+'(z0, z1))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1))))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c10_1, c11_1, c6_2, c6_1, c_1, c7_1, c8_1


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

(163) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(pair(z0, z1)) -> c10(+'(z0, q(pair(z0, z1)))) by 
   H(pair(z0, z1)) -> c10(+'(z0, z1))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c11_1, c6_2, c6_1, c_1, c7_1, c8_1, c10_1


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(pair(z0, z1)) -> c11(+'(p(pair(z0, z1)), z1)) by 
   H(pair(z0, z1)) -> c11(+'(z0, z1))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1))))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, H_1, F_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c11_1, c6_2, c6_1, c_1, c7_1, c8_1, c10_1


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

(167) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace H(pair(z0, z1)) -> c11(+'(z0, q(pair(z0, z1)))) by 
   H(pair(z0, z1)) -> c11(+'(z0, z1))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(s(s(z0))) -> c6(H(h(g(z0))), G(s(z0))) by 
   G(s(s(x0))) -> c6(H(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), G(s(x0)))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(h(g(z0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(171) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(s(z0)))) -> c(H(h(g(z0)))) by 
   F(s(s(s(x0)))) -> c(H(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(0))) -> c(+'(p(g(0)), q(pair(s(0), s(0))))) by 
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(h(g(z0))))) by 
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))) by 
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(g(0)))) by 
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(g(s(z0))))) by 
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(183) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0))))) by 
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(185) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(s(s(0))) -> c7(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0))) by G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))), G(s(0)))
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))), G(s(0)))
S tuples:
   +'(z0, s(z1)) -> c16(+'(z0, z1))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   +'_2, G_1, F_1, H_1

Compound Symbols:   c16_1, c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1


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

(187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace +'(z0, s(z1)) -> c16(+'(z0, z1)) by 
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c7(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), G(s(z0)))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))), G(s(0)))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   F(s(s(z0))) -> c(+'(p(g(z0)), q(g(z0))))
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c9_1, c7_2, c8_2, c6_2, c6_1, c_1, c7_1, c8_1, c10_1, c11_1, c16_1


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

(189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   G(s(0)) -> c8(+'(p(g(0)), s(0)))
   F(s(s(0))) -> c(+'(p(g(0)), s(0)))
   G(s(0)) -> c7(+'(p(g(0)), s(0)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(z0)) -> c9(G(z0))
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))), G(s(0)))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(z0)) -> c9(G(z0))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c9_1, c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1


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

(191) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(s(z0)) -> c9(G(z0)) by 
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c7(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(h(pair(s(0), s(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))), G(s(0)))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(0))) -> c8(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(0))) -> c6(H(h(pair(s(0), s(0)))), G(s(0)))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   G(s(s(0))) -> c7(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))), G(s(0)))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1


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

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1


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

(195) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0))))) by G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1


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

(197) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1


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

(199) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(s(0)) -> c7(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0))))) by G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))
----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1


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

(201) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   G(s(0)) -> c7(+'(p(pair(s(0), s(0))), s(0)))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c7(+'(s(0), q(g(0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c7_1, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1


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

(203) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(s(0)) -> c7(+'(s(0), q(g(0)))) by G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
----------------------------------------

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1, c7_1


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

(205) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0))))) by G(s(0)) -> c8(+'(p(pair(s(0), s(0))), s(0)))
----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), s(0)))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1, c7_1


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

(207) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), s(0)))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1, c7_1


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

(209) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace H(pair(z0, z1)) -> c10(+'(z0, z1)) by 
   H(pair(z0, s(s(y1)))) -> c10(+'(z0, s(s(y1))))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c10(+'(z0, z1))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
   H(pair(z0, s(s(y1)))) -> c10(+'(z0, s(s(y1))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c10_1, c11_1, c16_1, c9_1, c1_1, c7_1


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

(211) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace H(pair(z0, z1)) -> c10(+'(z0, z1)) by 
   H(pair(z0, s(s(y1)))) -> c10(+'(z0, s(s(y1))))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
   H(pair(z0, s(s(y1)))) -> c10(+'(z0, s(s(y1))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c11_1, c16_1, c9_1, c1_1, c7_1, c10_1


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

(213) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace H(pair(z0, z1)) -> c11(+'(z0, z1)) by 
   H(pair(z0, s(s(y1)))) -> c11(+'(z0, s(s(y1))))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   g(0) -> pair(s(0), s(0))
   g(s(z0)) -> h(g(z0))
   g(s(z0)) -> pair(+(p(g(z0)), q(g(z0))), p(g(z0)))
   h(z0) -> pair(+(p(z0), q(z0)), p(z0))
   +(z0, 0) -> z0
   +(z0, s(z1)) -> s(+(z0, z1))
   p(pair(z0, z1)) -> z0
   q(pair(z0, z1)) -> z1
Tuples:
   G(s(s(z0))) -> c6(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), G(s(z0)))
   G(s(0)) -> c6(H(pair(s(0), s(0))))
   F(s(s(s(z0)))) -> c(H(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c7(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c7(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c7(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c7(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c7(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(h(g(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(h(g(z0)))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(g(s(x0))), p(g(x0))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))), G(s(s(z0))))
   G(s(s(z0))) -> c8(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(z0))) -> c8(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(z0)))
   G(s(s(x0))) -> c8(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(h(h(g(z0)))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c8(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))), G(s(x0)))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c8(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))), G(s(s(z0))))
   G(s(0)) -> c8(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   G(s(0)) -> c8(+'(s(0), q(g(0))))
   H(pair(z0, z1)) -> c11(+'(z0, z1))
   G(s(s(s(z0)))) -> c6(H(h(h(g(z0)))), G(s(s(z0))))
   G(s(s(s(z0)))) -> c6(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), G(s(s(z0))))
   G(s(s(x0))) -> c6(G(s(x0)))
   F(s(s(s(0)))) -> c(H(h(pair(s(0), s(0)))))
   F(s(s(s(s(z0))))) -> c(H(h(h(g(z0)))))
   F(s(s(s(s(z0))))) -> c(H(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(p(pair(s(0), s(0))), q(pair(s(0), s(0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), q(pair(+(p(g(x0)), q(g(x0))), p(g(x0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(h(g(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(h(g(z0)))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(h(g(z0)))))
   F(s(s(s(x0)))) -> c(+'(p(g(s(x0))), p(g(x0))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(s(z0))))) -> c(+'(p(g(s(s(z0)))), q(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0)))))))
   F(s(s(s(0)))) -> c(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   F(s(s(s(z0)))) -> c(+'(p(h(g(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(s(z0)))) -> c(+'(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))))
   F(s(s(0))) -> c(+'(s(0), q(g(0))))
   F(s(s(s(x0)))) -> c(+'(p(pair(+(p(g(x0)), q(g(x0))), p(g(x0)))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(h(g(z0)))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(h(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(x0)))) -> c(+'(+(p(g(x0)), q(g(x0))), q(g(s(x0)))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(h(g(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(g(s(z0)))), p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(h(g(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(g(s(z0))), q(pair(+(p(g(z0)), q(g(z0))), p(g(z0))))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(0)))) -> c(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(h(g(z0))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   F(s(s(s(s(z0))))) -> c(+'(p(pair(+(p(pair(+(p(g(z0)), q(g(z0))), p(g(z0)))), q(g(s(z0)))), p(g(s(z0))))), q(g(s(s(z0))))))
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0)))))))
   G(s(s(0))) -> c1(G(s(0)))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0))))))
   G(s(s(0))) -> c1(+'(p(h(pair(s(0), s(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(g(0))), p(pair(s(0), s(0))))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(g(0)), q(pair(s(0), s(0)))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(pair(+(p(pair(s(0), s(0))), q(g(0))), p(g(0)))), q(g(s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(h(pair(s(0), s(0))))))
   G(s(s(0))) -> c1(H(h(pair(s(0), s(0)))))
   G(s(s(0))) -> c1(+'(p(g(s(0))), q(pair(+(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))))))
   G(s(0)) -> c7(+'(s(0), q(pair(s(0), s(0)))))
   H(pair(z0, s(s(y1)))) -> c10(+'(z0, s(s(y1))))
   H(pair(z0, s(s(y1)))) -> c11(+'(z0, s(s(y1))))
S tuples:
   +'(z0, s(s(y1))) -> c16(+'(z0, s(y1)))
K tuples:
   G(s(s(y0))) -> c9(G(s(y0)))
   G(s(s(s(y0)))) -> c9(G(s(s(y0))))
   G(s(s(0))) -> c9(G(s(0)))
   G(s(s(s(s(y0))))) -> c9(G(s(s(s(y0)))))
   G(s(s(s(0)))) -> c9(G(s(s(0))))
Defined Rule Symbols:   g_1, h_1, +_2, p_1, q_1

Defined Pair Symbols:   G_1, F_1, H_1, +'_2

Compound Symbols:   c6_2, c6_1, c_1, c7_2, c8_2, c8_1, c11_1, c16_1, c9_1, c1_1, c7_1, c10_1


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

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

(216)
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:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(x))) -> p(h(g(x))) [1]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(x)) -> h(g(x)) [1]
   h(x) -> pair(+(p(x), q(x)), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   +(x, 0) -> x [1]
   +(x, s(y)) -> s(+(x, y)) [1]
   f(s(s(x))) -> +(p(g(x)), q(g(x))) [1]
   g(s(x)) -> pair(+(p(g(x)), q(g(x))), p(g(x))) [1]

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

(217) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

+ => plus

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

(218)
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:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(x))) -> p(h(g(x))) [1]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(x)) -> h(g(x)) [1]
   h(x) -> pair(plus(p(x), q(x)), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   plus(x, 0) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   f(s(s(x))) -> plus(p(g(x)), q(g(x))) [1]
   g(s(x)) -> pair(plus(p(g(x)), q(g(x))), p(g(x))) [1]

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

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

(220)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(x))) -> p(h(g(x))) [1]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(x)) -> h(g(x)) [1]
   h(x) -> pair(plus(p(x), q(x)), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   plus(x, 0) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   f(s(s(x))) -> plus(p(g(x)), q(g(x))) [1]
   g(s(x)) -> pair(plus(p(g(x)), q(g(x))), p(g(x))) [1]

The TRS has the following type information:
f :: 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
p :: pair -> 0:s
h :: pair -> pair
g :: 0:s -> pair
pair :: 0:s -> 0:s -> pair
plus :: 0:s -> 0:s -> 0:s
q :: pair -> 0:s

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

(221) 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:

   f_1

(c) The following functions are completely defined:

   h_1
   g_1
   p_1
   q_1
   plus_2

Due to the following rules being added:

   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

And the following fresh constants:    const

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

(222)
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:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(x))) -> p(h(g(x))) [1]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(x)) -> h(g(x)) [1]
   h(x) -> pair(plus(p(x), q(x)), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   plus(x, 0) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   f(s(s(x))) -> plus(p(g(x)), q(g(x))) [1]
   g(s(x)) -> pair(plus(p(g(x)), q(g(x))), p(g(x))) [1]
   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

The TRS has the following type information:
f :: 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
p :: pair -> 0:s
h :: pair -> pair
g :: 0:s -> pair
pair :: 0:s -> 0:s -> pair
plus :: 0:s -> 0:s -> 0:s
q :: pair -> 0:s
const :: pair

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

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

(224)
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:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(0))) -> p(h(pair(s(0), s(0)))) [2]
   f(s(s(s(x')))) -> p(h(h(g(x')))) [2]
   f(s(s(s(x'')))) -> p(h(pair(plus(p(g(x'')), q(g(x''))), p(g(x''))))) [2]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(0)) -> h(pair(s(0), s(0))) [2]
   g(s(s(x1))) -> h(h(g(x1))) [2]
   g(s(s(x2))) -> h(pair(plus(p(g(x2)), q(g(x2))), p(g(x2)))) [2]
   h(pair(x3, y')) -> pair(plus(x3, y'), p(pair(x3, y'))) [3]
   h(pair(x3, y')) -> pair(plus(x3, 0), p(pair(x3, y'))) [2]
   h(pair(x4, y'')) -> pair(plus(0, y''), p(pair(x4, y''))) [2]
   h(x) -> pair(plus(0, 0), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   plus(x, 0) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   f(s(s(0))) -> plus(p(pair(s(0), s(0))), q(pair(s(0), s(0)))) [3]
   f(s(s(s(x5)))) -> plus(p(h(g(x5))), q(h(g(x5)))) [3]
   f(s(s(s(x5)))) -> plus(p(h(g(x5))), q(pair(plus(p(g(x5)), q(g(x5))), p(g(x5))))) [3]
   f(s(s(s(x6)))) -> plus(p(pair(plus(p(g(x6)), q(g(x6))), p(g(x6)))), q(h(g(x6)))) [3]
   f(s(s(s(x6)))) -> plus(p(pair(plus(p(g(x6)), q(g(x6))), p(g(x6)))), q(pair(plus(p(g(x6)), q(g(x6))), p(g(x6))))) [3]
   g(s(0)) -> pair(plus(p(pair(s(0), s(0))), q(pair(s(0), s(0)))), p(pair(s(0), s(0)))) [4]
   g(s(s(x7))) -> pair(plus(p(h(g(x7))), q(h(g(x7)))), p(h(g(x7)))) [4]
   g(s(s(x7))) -> pair(plus(p(h(g(x7))), q(h(g(x7)))), p(pair(plus(p(g(x7)), q(g(x7))), p(g(x7))))) [4]
   g(s(s(x7))) -> pair(plus(p(h(g(x7))), q(pair(plus(p(g(x7)), q(g(x7))), p(g(x7))))), p(h(g(x7)))) [4]
   g(s(s(x7))) -> pair(plus(p(h(g(x7))), q(pair(plus(p(g(x7)), q(g(x7))), p(g(x7))))), p(pair(plus(p(g(x7)), q(g(x7))), p(g(x7))))) [4]
   g(s(s(x8))) -> pair(plus(p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8)))), q(h(g(x8)))), p(h(g(x8)))) [4]
   g(s(s(x8))) -> pair(plus(p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8)))), q(h(g(x8)))), p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8))))) [4]
   g(s(s(x8))) -> pair(plus(p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8)))), q(pair(plus(p(g(x8)), q(g(x8))), p(g(x8))))), p(h(g(x8)))) [4]
   g(s(s(x8))) -> pair(plus(p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8)))), q(pair(plus(p(g(x8)), q(g(x8))), p(g(x8))))), p(pair(plus(p(g(x8)), q(g(x8))), p(g(x8))))) [4]
   p(v0) -> 0 [0]
   q(v0) -> 0 [0]

The TRS has the following type information:
f :: 0:s -> 0:s
0 :: 0:s
s :: 0:s -> 0:s
p :: pair -> 0:s
h :: pair -> pair
g :: 0:s -> pair
pair :: 0:s -> 0:s -> pair
plus :: 0:s -> 0:s -> 0:s
q :: pair -> 0:s
const :: pair

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

(225) 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
   const => 0

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

(226)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 3 }-> plus(p(h(g(x5))), q(h(g(x5)))) :|: z = 1 + (1 + (1 + x5)), x5 >= 0
   f(z) -{ 3 }-> plus(p(h(g(x5))), q(1 + plus(p(g(x5)), q(g(x5))) + p(g(x5)))) :|: z = 1 + (1 + (1 + x5)), x5 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6))), q(h(g(x6)))) :|: x6 >= 0, z = 1 + (1 + (1 + x6))
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6))), q(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6)))) :|: x6 >= 0, z = 1 + (1 + (1 + x6))
   f(z) -{ 3 }-> plus(p(1 + (1 + 0) + (1 + 0)), q(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 2 }-> p(h(h(g(x')))) :|: z = 1 + (1 + (1 + x')), x' >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(x'')), q(g(x''))) + p(g(x'')))) :|: x'' >= 0, z = 1 + (1 + (1 + x''))
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(x1))) :|: z = 1 + (1 + x1), x1 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(x2)), q(g(x2))) + p(g(x2))) :|: z = 1 + (1 + x2), x2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(h(g(x7)))) + p(h(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(h(g(x7)))) + p(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7)))) + p(h(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7)))) + p(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(h(g(x8)))) + p(h(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(h(g(x8)))) + p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8)))) + p(h(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8)))) + p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + (1 + 0) + (1 + 0)), q(1 + (1 + 0) + (1 + 0))) + p(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + p(1 + x3 + y') :|: y' >= 0, z = 1 + x3 + y', x3 >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + p(1 + x3 + y') :|: y' >= 0, z = 1 + x3 + y', x3 >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + p(1 + x4 + y'') :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + p(x) :|: x >= 0, z = x
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = x
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0

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

(228)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(x5))), q(h(g(x5)))) :|: z = 1 + (1 + (1 + x5)), x5 >= 0
   f(z) -{ 3 }-> plus(p(h(g(x5))), q(1 + plus(p(g(x5)), q(g(x5))) + p(g(x5)))) :|: z = 1 + (1 + (1 + x5)), x5 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6))), q(h(g(x6)))) :|: x6 >= 0, z = 1 + (1 + (1 + x6))
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6))), q(1 + plus(p(g(x6)), q(g(x6))) + p(g(x6)))) :|: x6 >= 0, z = 1 + (1 + (1 + x6))
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(x')))) :|: z = 1 + (1 + (1 + x')), x' >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(x'')), q(g(x''))) + p(g(x'')))) :|: x'' >= 0, z = 1 + (1 + (1 + x''))
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(x1))) :|: z = 1 + (1 + x1), x1 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(x2)), q(g(x2))) + p(g(x2))) :|: z = 1 + (1 + x2), x2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(h(g(x7)))) + p(h(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(h(g(x7)))) + p(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7)))) + p(h(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(h(g(x7))), q(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7)))) + p(1 + plus(p(g(x7)), q(g(x7))) + p(g(x7))) :|: x7 >= 0, z = 1 + (1 + x7)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(h(g(x8)))) + p(h(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(h(g(x8)))) + p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8)))) + p(h(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))), q(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8)))) + p(1 + plus(p(g(x8)), q(g(x8))) + p(g(x8))) :|: x8 >= 0, z = 1 + (1 + x8)
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: x >= 0, z = x, x = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: x >= 0, z = x, v0 >= 0, x = v0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = x
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

(230)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0


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(231) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { plus }
   { q }
   { p }
   { h }
   { g }
   { f }

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(232)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {q}, {p}, {h}, {g}, {f}

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(233) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(234)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {q}, {p}, {h}, {g}, {f}

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(235) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

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(236)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {plus}, {q}, {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: ?, size: O(n^1) [z + z']

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(237) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z'

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(238)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 }-> plus(x, y') :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> plus(x, 0) :|: z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 4 }-> plus(0, y) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 3 }-> plus(0, 0) :|: z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 6 }-> 1 + plus(x, y') + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 7 }-> 1 + plus(x, y'') + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + plus(x, 0) + x' :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 5 }-> 1 + plus(x, 0) + 0 :|: z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 5 }-> 1 + plus(0, y) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 6 }-> 1 + plus(0, y') + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + plus(0, 0) + x :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 4 }-> 1 + plus(0, 0) + 0 :|: z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 4 }-> 1 + plus(x3, y') + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + plus(x3, y') + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(x3, 0) + x :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(x3, 0) + 0 :|: y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 3 }-> 1 + plus(0, y'') + x :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 2 }-> 1 + plus(0, y'') + 0 :|: z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 2 }-> 1 + plus(0, 0) + x' :|: z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 1 }-> 1 + plus(0, 0) + 0 :|: z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 }-> 1 + plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']

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(239) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(240)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']

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

(241) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: q
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(242)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {q}, {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: ?, size: O(n^1) [z]

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

(243) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: q
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(244)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]

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

(245) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(246)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]

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

(247) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(248)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {p}, {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: ?, size: O(n^1) [z]

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

(249) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(250)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]

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(251) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(252)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]

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

(253) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: h
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 2*z

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

(254)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {h}, {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]
  h: runtime: ?, size: O(n^1) [1 + 2*z]

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(255) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: h
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + z

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

(256)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + (1 + 0) + (1 + 0))) :|: z = 1 + (1 + 0)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + (1 + 0) + (1 + 0)) :|: z = 1 + 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]
  h: runtime: O(n^1) [4 + z], size: O(n^1) [1 + 2*z]

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

(257) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(258)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 10 }-> s21 :|: s20 >= 0, s20 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), s21 >= 0, s21 <= s20, z = 1 + (1 + 0)
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 9 }-> s19 :|: s19 >= 0, s19 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]
  h: runtime: O(n^1) [4 + z], size: O(n^1) [1 + 2*z]

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

(259) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: g
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

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

(260)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 10 }-> s21 :|: s20 >= 0, s20 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), s21 >= 0, s21 <= s20, z = 1 + (1 + 0)
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 9 }-> s19 :|: s19 >= 0, s19 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]
  h: runtime: O(n^1) [4 + z], size: O(n^1) [1 + 2*z]
  g: runtime: ?, size: EXP

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

(261) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

(262)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 5 + y }-> s10 :|: s10 >= 0, s10 <= 0 + y, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 10 }-> s21 :|: s20 >= 0, s20 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), s21 >= 0, s21 <= s20, z = 1 + (1 + 0)
   f(z) -{ 5 }-> s7 :|: s7 >= 0, s7 <= x + 0, z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   f(z) -{ 6 + y' }-> s8 :|: s8 >= 0, s8 <= x + y', z = 1 + (1 + 0), 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   f(z) -{ 4 }-> s9 :|: s9 >= 0, s9 <= 0 + 0, z = 1 + (1 + 0), v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(h(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 3 }-> plus(p(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3))), q(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(h(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 2 }-> p(h(1 + plus(p(g(z - 3)), q(g(z - 3))) + p(g(z - 3)))) :|: z - 3 >= 0
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 9 }-> s19 :|: s19 >= 0, s19 <= 1 + 2 * (1 + (1 + 0) + (1 + 0)), z = 1 + 0
   g(z) -{ 2 }-> h(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 2 }-> h(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 7 }-> 1 + s11 + x' :|: s11 >= 0, s11 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0
   g(z) -{ 8 + y'' }-> 1 + s12 + x' :|: s12 >= 0, s12 <= x + y'', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x'' + y'', x'' >= 0, y'' >= 0
   g(z) -{ 6 }-> 1 + s13 + 0 :|: s13 >= 0, s13 <= x + 0, z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s14 + 0 :|: s14 >= 0, s14 <= x + y', z = 1 + 0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 6 }-> 1 + s15 + x :|: s15 >= 0, s15 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0'
   g(z) -{ 7 + y' }-> 1 + s16 + x :|: s16 >= 0, s16 <= 0 + y', z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0, 1 + (1 + 0) + (1 + 0) = 1 + x' + y', x' >= 0, y' >= 0
   g(z) -{ 5 }-> 1 + s17 + 0 :|: s17 >= 0, s17 <= 0 + 0, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', v0'' >= 0, 1 + (1 + 0) + (1 + 0) = v0''
   g(z) -{ 6 + y }-> 1 + s18 + 0 :|: s18 >= 0, s18 <= 0 + y, z = 1 + 0, v0 >= 0, 1 + (1 + 0) + (1 + 0) = v0, v0' >= 0, 1 + (1 + 0) + (1 + 0) = v0', 1 + (1 + 0) + (1 + 0) = 1 + x + y, x >= 0, y >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(h(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(h(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(h(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 4 }-> 1 + plus(p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))), q(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2)))) + p(1 + plus(p(g(z - 2)), q(g(z - 2))) + p(g(z - 2))) :|: z - 2 >= 0
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 5 + y' }-> 1 + s' + x :|: s' >= 0, s' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 4 + y' }-> 1 + s'' + 0 :|: s'' >= 0, s'' <= x3 + y', y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 }-> 1 + s1 + x :|: s1 >= 0, s1 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, 1 + x3 + y' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 }-> 1 + s2 + 0 :|: s2 >= 0, s2 <= x3 + 0, y' >= 0, z = 1 + x3 + y', x3 >= 0, v0 >= 0, 1 + x3 + y' = v0
   h(z) -{ 4 + y'' }-> 1 + s3 + x :|: s3 >= 0, s3 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, 1 + x4 + y'' = 1 + x + y, x >= 0, y >= 0
   h(z) -{ 3 + y'' }-> 1 + s4 + 0 :|: s4 >= 0, s4 <= 0 + y'', z = 1 + x4 + y'', x4 >= 0, y'' >= 0, v0 >= 0, 1 + x4 + y'' = v0
   h(z) -{ 3 }-> 1 + s5 + x' :|: s5 >= 0, s5 <= 0 + 0, z >= 0, z = 1 + x' + y, x' >= 0, y >= 0
   h(z) -{ 2 }-> 1 + s6 + 0 :|: s6 >= 0, s6 <= 0 + 0, z >= 0
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   plus(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   plus(z, z') -{ 1 + z' }-> 1 + s :|: s >= 0, s <= z + (z' - 1), z >= 0, z' - 1 >= 0
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: z >= 0

Function symbols to be analyzed: {g}, {f}
Previous analysis results are:
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z + z']
  q: runtime: O(1) [1], size: O(n^1) [z]
  p: runtime: O(1) [1], size: O(n^1) [z]
  h: runtime: O(n^1) [4 + z], size: O(n^1) [1 + 2*z]
  g: runtime: INF, size: EXP

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(263) 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:

   p(v0) -> null_p [0]
   q(v0) -> null_q [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]
   plus(v0, v1) -> null_plus [0]

And the following fresh constants:    null_p, null_q, null_f, null_g, null_plus

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(264)
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:

   f(0) -> 0 [1]
   f(s(0)) -> s(0) [1]
   f(s(s(x))) -> p(h(g(x))) [1]
   g(0) -> pair(s(0), s(0)) [1]
   g(s(x)) -> h(g(x)) [1]
   h(x) -> pair(plus(p(x), q(x)), p(x)) [1]
   p(pair(x, y)) -> x [1]
   q(pair(x, y)) -> y [1]
   plus(x, 0) -> x [1]
   plus(x, s(y)) -> s(plus(x, y)) [1]
   f(s(s(x))) -> plus(p(g(x)), q(g(x))) [1]
   g(s(x)) -> pair(plus(p(g(x)), q(g(x))), p(g(x))) [1]
   p(v0) -> null_p [0]
   q(v0) -> null_q [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]
   plus(v0, v1) -> null_plus [0]

The TRS has the following type information:
f :: 0:s:null_p:null_q:null_f:null_plus -> 0:s:null_p:null_q:null_f:null_plus
0 :: 0:s:null_p:null_q:null_f:null_plus
s :: 0:s:null_p:null_q:null_f:null_plus -> 0:s:null_p:null_q:null_f:null_plus
p :: pair:null_g -> 0:s:null_p:null_q:null_f:null_plus
h :: pair:null_g -> pair:null_g
g :: 0:s:null_p:null_q:null_f:null_plus -> pair:null_g
pair :: 0:s:null_p:null_q:null_f:null_plus -> 0:s:null_p:null_q:null_f:null_plus -> pair:null_g
plus :: 0:s:null_p:null_q:null_f:null_plus -> 0:s:null_p:null_q:null_f:null_plus -> 0:s:null_p:null_q:null_f:null_plus
q :: pair:null_g -> 0:s:null_p:null_q:null_f:null_plus
null_p :: 0:s:null_p:null_q:null_f:null_plus
null_q :: 0:s:null_p:null_q:null_f:null_plus
null_f :: 0:s:null_p:null_q:null_f:null_plus
null_g :: pair:null_g
null_plus :: 0:s:null_p:null_q:null_f:null_plus

Rewrite Strategy: INNERMOST
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(265) 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
   null_p => 0
   null_q => 0
   null_f => 0
   null_g => 0
   null_plus => 0

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(266)
Obligation:
Complexity RNTS consisting of the following rules:

   f(z) -{ 1 }-> plus(p(g(x)), q(g(x))) :|: x >= 0, z = 1 + (1 + x)
   f(z) -{ 1 }-> p(h(g(x))) :|: x >= 0, z = 1 + (1 + x)
   f(z) -{ 1 }-> 0 :|: z = 0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 1 }-> 1 + 0 :|: z = 1 + 0
   g(z) -{ 1 }-> h(g(x)) :|: x >= 0, z = 1 + x
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 1 }-> 1 + plus(p(g(x)), q(g(x))) + p(g(x)) :|: x >= 0, z = 1 + x
   g(z) -{ 1 }-> 1 + (1 + 0) + (1 + 0) :|: z = 0
   h(z) -{ 1 }-> 1 + plus(p(x), q(x)) + p(x) :|: x >= 0, z = x
   p(z) -{ 1 }-> x :|: z = 1 + x + y, x >= 0, y >= 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   plus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = x
   q(z) -{ 1 }-> y :|: z = 1 + x + y, x >= 0, y >= 0
   q(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

Only complete derivations are relevant for the runtime complexity.