WORST_CASE(Omega(n^1),O(n^1))
proof of input_XMGfBc5HLm.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (4) CdtProblem
    (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTRS
    (9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxWeightedTrs
    (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedTrs
    (13) CompletionProof [UPPER BOUND(ID), 0 ms]
    (14) CpxTypedWeightedCompleteTrs
    (15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxTypedWeightedCompleteTrs
    (17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (18) CpxRNTS
    (19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRNTS
    (21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxRNTS
    (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 186 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 72 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 97 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (34) CpxRNTS
    (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 230 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (40) CpxRNTS
    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 26 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 32 ms]
    (46) CpxRNTS
    (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 190 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (52) CpxRNTS
    (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 186 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (58) CpxRNTS
    (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 279 ms]
    (62) CpxRNTS
    (63) IntTrsBoundProof [UPPER BOUND(ID), 103 ms]
    (64) CpxRNTS
    (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 136 ms]
    (68) CpxRNTS
    (69) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (70) CpxRNTS
    (71) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 269 ms]
    (74) CpxRNTS
    (75) IntTrsBoundProof [UPPER BOUND(ID), 124 ms]
    (76) CpxRNTS
    (77) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 46 ms]
    (80) CpxRNTS
    (81) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (82) CpxRNTS
    (83) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (84) CpxRNTS
    (85) IntTrsBoundProof [UPPER BOUND(ID), 317 ms]
    (86) CpxRNTS
    (87) IntTrsBoundProof [UPPER BOUND(ID), 104 ms]
    (88) CpxRNTS
    (89) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (90) CpxRNTS
    (91) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
    (92) CpxRNTS
    (93) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (94) CpxRNTS
    (95) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (96) CpxRNTS
    (97) IntTrsBoundProof [UPPER BOUND(ID), 327 ms]
    (98) CpxRNTS
    (99) IntTrsBoundProof [UPPER BOUND(ID), 105 ms]
    (100) CpxRNTS
    (101) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (102) CpxRNTS
    (103) IntTrsBoundProof [UPPER BOUND(ID), 137 ms]
    (104) CpxRNTS
    (105) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (106) CpxRNTS
    (107) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (108) CpxRNTS
    (109) IntTrsBoundProof [UPPER BOUND(ID), 317 ms]
    (110) CpxRNTS
    (111) IntTrsBoundProof [UPPER BOUND(ID), 94 ms]
    (112) CpxRNTS
    (113) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (114) CpxRNTS
    (115) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
    (116) CpxRNTS
    (117) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (118) CpxRNTS
    (119) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (120) CpxRNTS
    (121) IntTrsBoundProof [UPPER BOUND(ID), 307 ms]
    (122) CpxRNTS
    (123) IntTrsBoundProof [UPPER BOUND(ID), 102 ms]
    (124) CpxRNTS
    (125) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (126) CpxRNTS
    (127) IntTrsBoundProof [UPPER BOUND(ID), 198 ms]
    (128) CpxRNTS
    (129) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (130) CpxRNTS
    (131) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (132) CpxRNTS
    (133) IntTrsBoundProof [UPPER BOUND(ID), 318 ms]
    (134) CpxRNTS
    (135) IntTrsBoundProof [UPPER BOUND(ID), 103 ms]
    (136) CpxRNTS
    (137) FinalProof [FINISHED, 0 ms]
    (138) BOUNDS(1, n^1)
(139) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms]
(140) CdtProblem
    (141) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CpxRelTRS
    (143) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CpxRelTRS
    (145) TypeInferenceProof [BOTH BOUNDS(ID, ID), 10 ms]
    (146) typed CpxTrs
    (147) OrderProof [LOWER BOUND(ID), 0 ms]
    (148) typed CpxTrs
    (149) RewriteLemmaProof [LOWER BOUND(ID), 443 ms]
    (150) BEST
        (151) proven lower bound
            (152) LowerBoundPropagationProof [FINISHED, 0 ms]
            (153) BOUNDS(n^1, INF)
        (154) typed CpxTrs
            (155) RewriteLemmaProof [LOWER BOUND(ID), 183 ms]
            (156) typed CpxTrs
            (157) RewriteLemmaProof [LOWER BOUND(ID), 149 ms]
            (158) typed CpxTrs
            (159) RewriteLemmaProof [LOWER BOUND(ID), 127 ms]
            (160) typed CpxTrs
            (161) RewriteLemmaProof [LOWER BOUND(ID), 136 ms]
            (162) typed CpxTrs
            (163) RewriteLemmaProof [LOWER BOUND(ID), 74 ms]
            (164) typed CpxTrs
            (165) RewriteLemmaProof [LOWER BOUND(ID), 112 ms]
            (166) typed CpxTrs
            (167) RewriteLemmaProof [LOWER BOUND(ID), 154 ms]
            (168) typed CpxTrs
            (169) RewriteLemmaProof [LOWER BOUND(ID), 142 ms]
            (170) typed CpxTrs
            (171) RewriteLemmaProof [LOWER BOUND(ID), 175 ms]
            (172) typed CpxTrs
            (173) RewriteLemmaProof [LOWER BOUND(ID), 330 ms]
            (174) typed CpxTrs


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

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

   f_0(x) -> a
   f_1(x) -> g_1(x, x)
   g_1(s(x), y) -> b(f_0(y), g_1(x, y))
   f_2(x) -> g_2(x, x)
   g_2(s(x), y) -> b(f_1(y), g_2(x, y))
   f_3(x) -> g_3(x, x)
   g_3(s(x), y) -> b(f_2(y), g_3(x, y))
   f_4(x) -> g_4(x, x)
   g_4(s(x), y) -> b(f_3(y), g_4(x, y))
   f_5(x) -> g_5(x, x)
   g_5(s(x), y) -> b(f_4(y), g_5(x, y))
   f_6(x) -> g_6(x, x)
   g_6(s(x), y) -> b(f_5(y), g_6(x, y))
   f_7(x) -> g_7(x, x)
   g_7(s(x), y) -> b(f_6(y), g_7(x, y))
   f_8(x) -> g_8(x, x)
   g_8(s(x), y) -> b(f_7(y), g_8(x, y))
   f_9(x) -> g_9(x, x)
   g_9(s(x), y) -> b(f_8(y), g_9(x, y))
   f_10(x) -> g_10(x, x)
   g_10(s(x), y) -> b(f_9(y), g_10(x, y))

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

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

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))
Tuples:
   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
S tuples:
   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
K tuples:none
Defined Rule Symbols:   f_0_1, f_1_1, g_1_2, f_2_1, g_2_2, f_3_1, g_3_2, f_4_1, g_4_2, f_5_1, g_5_2, f_6_1, g_6_2, f_7_1, g_7_2, f_8_1, g_8_2, f_9_1, g_9_2, f_10_1, g_10_2

Defined Pair Symbols:   F_0_1, F_1_1, G_1_2, F_2_1, G_2_2, F_3_1, G_3_2, F_4_1, G_4_2, F_5_1, G_5_2, F_6_1, G_6_2, F_7_1, G_7_2, F_8_1, G_8_2, F_9_1, G_9_2, F_10_1, G_10_2

Compound Symbols:   c, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1


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

(3) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   F_10(z0) -> c28(G_10(z0, z0))
Removed 2 trailing nodes:
   F_0(z0) -> c
   G_1(s(z0), z1) -> c2(F_0(z1))

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

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))
Tuples:
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
S tuples:
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
K tuples:none
Defined Rule Symbols:   f_0_1, f_1_1, g_1_2, f_2_1, g_2_2, f_3_1, g_3_2, f_4_1, g_4_2, f_5_1, g_5_2, f_6_1, g_6_2, f_7_1, g_7_2, f_8_1, g_8_2, f_9_1, g_9_2, f_10_1, g_10_2

Defined Pair Symbols:   F_1_1, G_1_2, F_2_1, G_2_2, F_3_1, G_3_2, F_4_1, G_4_2, F_5_1, G_5_2, F_6_1, G_6_2, F_7_1, G_7_2, F_8_1, G_8_2, F_9_1, G_9_2, G_10_2

Compound Symbols:   c1_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c29_1, c30_1


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

(5) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:none
Tuples:
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
S tuples:
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:   F_1_1, G_1_2, F_2_1, G_2_2, F_3_1, G_3_2, F_4_1, G_4_2, F_5_1, G_5_2, F_6_1, G_6_2, F_7_1, G_7_2, F_8_1, G_8_2, F_9_1, G_9_2, G_10_2

Compound Symbols:   c1_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c29_1, c30_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 CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))

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

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

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


The TRS R consists of the following rules:

   F_1(z0) -> c1(G_1(z0, z0)) [1]
   G_1(s(z0), z1) -> c3(G_1(z0, z1)) [1]
   F_2(z0) -> c4(G_2(z0, z0)) [1]
   G_2(s(z0), z1) -> c5(F_1(z1)) [1]
   G_2(s(z0), z1) -> c6(G_2(z0, z1)) [1]
   F_3(z0) -> c7(G_3(z0, z0)) [1]
   G_3(s(z0), z1) -> c8(F_2(z1)) [1]
   G_3(s(z0), z1) -> c9(G_3(z0, z1)) [1]
   F_4(z0) -> c10(G_4(z0, z0)) [1]
   G_4(s(z0), z1) -> c11(F_3(z1)) [1]
   G_4(s(z0), z1) -> c12(G_4(z0, z1)) [1]
   F_5(z0) -> c13(G_5(z0, z0)) [1]
   G_5(s(z0), z1) -> c14(F_4(z1)) [1]
   G_5(s(z0), z1) -> c15(G_5(z0, z1)) [1]
   F_6(z0) -> c16(G_6(z0, z0)) [1]
   G_6(s(z0), z1) -> c17(F_5(z1)) [1]
   G_6(s(z0), z1) -> c18(G_6(z0, z1)) [1]
   F_7(z0) -> c19(G_7(z0, z0)) [1]
   G_7(s(z0), z1) -> c20(F_6(z1)) [1]
   G_7(s(z0), z1) -> c21(G_7(z0, z1)) [1]
   F_8(z0) -> c22(G_8(z0, z0)) [1]
   G_8(s(z0), z1) -> c23(F_7(z1)) [1]
   G_8(s(z0), z1) -> c24(G_8(z0, z1)) [1]
   F_9(z0) -> c25(G_9(z0, z0)) [1]
   G_9(s(z0), z1) -> c26(F_8(z1)) [1]
   G_9(s(z0), z1) -> c27(G_9(z0, z1)) [1]
   G_10(s(z0), z1) -> c29(F_9(z1)) [1]
   G_10(s(z0), z1) -> c30(G_10(z0, z1)) [1]

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

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

(12)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   F_1(z0) -> c1(G_1(z0, z0)) [1]
   G_1(s(z0), z1) -> c3(G_1(z0, z1)) [1]
   F_2(z0) -> c4(G_2(z0, z0)) [1]
   G_2(s(z0), z1) -> c5(F_1(z1)) [1]
   G_2(s(z0), z1) -> c6(G_2(z0, z1)) [1]
   F_3(z0) -> c7(G_3(z0, z0)) [1]
   G_3(s(z0), z1) -> c8(F_2(z1)) [1]
   G_3(s(z0), z1) -> c9(G_3(z0, z1)) [1]
   F_4(z0) -> c10(G_4(z0, z0)) [1]
   G_4(s(z0), z1) -> c11(F_3(z1)) [1]
   G_4(s(z0), z1) -> c12(G_4(z0, z1)) [1]
   F_5(z0) -> c13(G_5(z0, z0)) [1]
   G_5(s(z0), z1) -> c14(F_4(z1)) [1]
   G_5(s(z0), z1) -> c15(G_5(z0, z1)) [1]
   F_6(z0) -> c16(G_6(z0, z0)) [1]
   G_6(s(z0), z1) -> c17(F_5(z1)) [1]
   G_6(s(z0), z1) -> c18(G_6(z0, z1)) [1]
   F_7(z0) -> c19(G_7(z0, z0)) [1]
   G_7(s(z0), z1) -> c20(F_6(z1)) [1]
   G_7(s(z0), z1) -> c21(G_7(z0, z1)) [1]
   F_8(z0) -> c22(G_8(z0, z0)) [1]
   G_8(s(z0), z1) -> c23(F_7(z1)) [1]
   G_8(s(z0), z1) -> c24(G_8(z0, z1)) [1]
   F_9(z0) -> c25(G_9(z0, z0)) [1]
   G_9(s(z0), z1) -> c26(F_8(z1)) [1]
   G_9(s(z0), z1) -> c27(G_9(z0, z1)) [1]
   G_10(s(z0), z1) -> c29(F_9(z1)) [1]
   G_10(s(z0), z1) -> c30(G_10(z0, z1)) [1]

The TRS has the following type information:
F_1 :: s -> c1
c1 :: c3 -> c1
G_1 :: s -> s -> c3
s :: s -> s
c3 :: c3 -> c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30

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

(13) 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_1
   G_1_2
   F_2_1
   G_2_2
   F_3_1
   G_3_2
   F_4_1
   G_4_2
   F_5_1
   G_5_2
   F_6_1
   G_6_2
   F_7_1
   G_7_2
   F_8_1
   G_8_2
   F_9_1
   G_9_2
   G_10_2

(c) The following functions are completely defined:
none

Due to the following rules being added:
none

And the following fresh constants:    const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10, const11, const12, const13, const14, const15, const16, const17, const18, const19

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

(14)
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_1(z0) -> c1(G_1(z0, z0)) [1]
   G_1(s(z0), z1) -> c3(G_1(z0, z1)) [1]
   F_2(z0) -> c4(G_2(z0, z0)) [1]
   G_2(s(z0), z1) -> c5(F_1(z1)) [1]
   G_2(s(z0), z1) -> c6(G_2(z0, z1)) [1]
   F_3(z0) -> c7(G_3(z0, z0)) [1]
   G_3(s(z0), z1) -> c8(F_2(z1)) [1]
   G_3(s(z0), z1) -> c9(G_3(z0, z1)) [1]
   F_4(z0) -> c10(G_4(z0, z0)) [1]
   G_4(s(z0), z1) -> c11(F_3(z1)) [1]
   G_4(s(z0), z1) -> c12(G_4(z0, z1)) [1]
   F_5(z0) -> c13(G_5(z0, z0)) [1]
   G_5(s(z0), z1) -> c14(F_4(z1)) [1]
   G_5(s(z0), z1) -> c15(G_5(z0, z1)) [1]
   F_6(z0) -> c16(G_6(z0, z0)) [1]
   G_6(s(z0), z1) -> c17(F_5(z1)) [1]
   G_6(s(z0), z1) -> c18(G_6(z0, z1)) [1]
   F_7(z0) -> c19(G_7(z0, z0)) [1]
   G_7(s(z0), z1) -> c20(F_6(z1)) [1]
   G_7(s(z0), z1) -> c21(G_7(z0, z1)) [1]
   F_8(z0) -> c22(G_8(z0, z0)) [1]
   G_8(s(z0), z1) -> c23(F_7(z1)) [1]
   G_8(s(z0), z1) -> c24(G_8(z0, z1)) [1]
   F_9(z0) -> c25(G_9(z0, z0)) [1]
   G_9(s(z0), z1) -> c26(F_8(z1)) [1]
   G_9(s(z0), z1) -> c27(G_9(z0, z1)) [1]
   G_10(s(z0), z1) -> c29(F_9(z1)) [1]
   G_10(s(z0), z1) -> c30(G_10(z0, z1)) [1]

The TRS has the following type information:
F_1 :: s -> c1
c1 :: c3 -> c1
G_1 :: s -> s -> c3
s :: s -> s
c3 :: c3 -> c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
const :: c1
const1 :: s
const2 :: c3
const3 :: c4
const4 :: c5:c6
const5 :: c7
const6 :: c8:c9
const7 :: c10
const8 :: c11:c12
const9 :: c13
const10 :: c14:c15
const11 :: c16
const12 :: c17:c18
const13 :: c19
const14 :: c20:c21
const15 :: c22
const16 :: c23:c24
const17 :: c25
const18 :: c26:c27
const19 :: c29:c30

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

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

(16)
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_1(z0) -> c1(G_1(z0, z0)) [1]
   G_1(s(z0), z1) -> c3(G_1(z0, z1)) [1]
   F_2(z0) -> c4(G_2(z0, z0)) [1]
   G_2(s(z0), z1) -> c5(F_1(z1)) [1]
   G_2(s(z0), z1) -> c6(G_2(z0, z1)) [1]
   F_3(z0) -> c7(G_3(z0, z0)) [1]
   G_3(s(z0), z1) -> c8(F_2(z1)) [1]
   G_3(s(z0), z1) -> c9(G_3(z0, z1)) [1]
   F_4(z0) -> c10(G_4(z0, z0)) [1]
   G_4(s(z0), z1) -> c11(F_3(z1)) [1]
   G_4(s(z0), z1) -> c12(G_4(z0, z1)) [1]
   F_5(z0) -> c13(G_5(z0, z0)) [1]
   G_5(s(z0), z1) -> c14(F_4(z1)) [1]
   G_5(s(z0), z1) -> c15(G_5(z0, z1)) [1]
   F_6(z0) -> c16(G_6(z0, z0)) [1]
   G_6(s(z0), z1) -> c17(F_5(z1)) [1]
   G_6(s(z0), z1) -> c18(G_6(z0, z1)) [1]
   F_7(z0) -> c19(G_7(z0, z0)) [1]
   G_7(s(z0), z1) -> c20(F_6(z1)) [1]
   G_7(s(z0), z1) -> c21(G_7(z0, z1)) [1]
   F_8(z0) -> c22(G_8(z0, z0)) [1]
   G_8(s(z0), z1) -> c23(F_7(z1)) [1]
   G_8(s(z0), z1) -> c24(G_8(z0, z1)) [1]
   F_9(z0) -> c25(G_9(z0, z0)) [1]
   G_9(s(z0), z1) -> c26(F_8(z1)) [1]
   G_9(s(z0), z1) -> c27(G_9(z0, z1)) [1]
   G_10(s(z0), z1) -> c29(F_9(z1)) [1]
   G_10(s(z0), z1) -> c30(G_10(z0, z1)) [1]

The TRS has the following type information:
F_1 :: s -> c1
c1 :: c3 -> c1
G_1 :: s -> s -> c3
s :: s -> s
c3 :: c3 -> c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
const :: c1
const1 :: s
const2 :: c3
const3 :: c4
const4 :: c5:c6
const5 :: c7
const6 :: c8:c9
const7 :: c10
const8 :: c11:c12
const9 :: c13
const10 :: c14:c15
const11 :: c16
const12 :: c17:c18
const13 :: c19
const14 :: c20:c21
const15 :: c22
const16 :: c23:c24
const17 :: c25
const18 :: c26:c27
const19 :: c29:c30

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

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

   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0
   const5 => 0
   const6 => 0
   const7 => 0
   const8 => 0
   const9 => 0
   const10 => 0
   const11 => 0
   const12 => 0
   const13 => 0
   const14 => 0
   const15 => 0
   const16 => 0
   const17 => 0
   const18 => 0
   const19 => 0

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

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z0, z0) :|: z = z0, z0 >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z0, z0) :|: z = z0, z0 >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z0, z0) :|: z = z0, z0 >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z0, z0) :|: z = z0, z0 >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z0, z0) :|: z = z0, z0 >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z0, z0) :|: z = z0, z0 >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z0, z0) :|: z = z0, z0 >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z0, z0) :|: z = z0, z0 >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z0, z0) :|: z = z0, z0 >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0


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

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

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z, z) :|: z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0


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

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

   { G_1 }
   { F_1 }
   { G_2 }
   { F_2 }
   { G_3 }
   { F_3 }
   { G_4 }
   { F_4 }
   { G_5 }
   { F_5 }
   { G_6 }
   { F_6 }
   { G_7 }
   { F_7 }
   { G_8 }
   { F_8 }
   { G_9 }
   { F_9 }
   { G_10 }

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

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z, z) :|: z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_1}, {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}

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

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

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z, z) :|: z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_1}, {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: G_1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

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

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z, z) :|: z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_1}, {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: ?, size: O(1) [0]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: G_1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 }-> 1 + G_1(z, z) :|: z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ 1 }-> 1 + G_1(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]

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

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

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

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_1}, {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: ?, size: O(1) [1]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + F_1(z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]

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

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_2}, {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: ?, size: O(n^1) [1 + z]

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z + z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 1 }-> 1 + G_2(z, z) :|: z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 1 }-> 1 + G_2(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]

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

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_2}, {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: ?, size: O(n^1) [2 + z]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + F_2(z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]

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

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

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_3
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z + z'

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

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_3}, {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: ?, size: O(n^1) [2 + z + z']

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_3
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + z + 2*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 1 }-> 1 + G_3(z, z) :|: z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 1 }-> 1 + G_3(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']

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

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_3
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_3}, {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: ?, size: O(n^1) [3 + 2*z]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_3
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 3*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + F_3(z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]

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

(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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_4
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + z + 2*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_4}, {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: ?, size: O(n^1) [3 + z + 2*z']

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_4
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + z + 3*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 1 }-> 1 + G_4(z, z) :|: z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 1 }-> 1 + G_4(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']

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

(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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']

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

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_4
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + 3*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_4}, {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: ?, size: O(n^1) [4 + 3*z]

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

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_4
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + 4*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + F_4(z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]

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

(73) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_5
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + z + 3*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_5}, {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: ?, size: O(n^1) [4 + z + 3*z']

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

(75) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_5
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 8 + z + 4*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 1 }-> 1 + G_5(z, z) :|: z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 1 }-> 1 + G_5(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']

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

(79) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_5
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + 4*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_5}, {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: ?, size: O(n^1) [5 + 4*z]

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

(81) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_5
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 5*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + F_5(z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]

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

(85) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_6
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 5 + z + 4*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_6}, {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: ?, size: O(n^1) [5 + z + 4*z']

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

(87) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_6
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 10 + z + 5*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 1 }-> 1 + G_6(z, z) :|: z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 1 }-> 1 + G_6(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']

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

(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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']

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

(91) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_6
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + 5*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_6}, {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: ?, size: O(n^1) [6 + 5*z]

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

(93) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_6
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 11 + 6*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + F_6(z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]

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

(97) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_7
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 6 + z + 5*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_7}, {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: ?, size: O(n^1) [6 + z + 5*z']

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

(99) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_7
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 12 + z + 6*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 1 }-> 1 + G_7(z, z) :|: z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 1 }-> 1 + G_7(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']

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

(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:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']

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

(103) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_7
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + 6*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_7}, {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: ?, size: O(n^1) [7 + 6*z]

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

(105) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_7
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 13 + 7*z

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + F_7(z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]

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

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

(108)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]

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

(109) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_8
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 7 + z + 6*z'

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

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

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_8}, {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: ?, size: O(n^1) [7 + z + 6*z']

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

(111) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_8
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 14 + z + 7*z'

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

(112)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 1 }-> 1 + G_8(z, z) :|: z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 1 }-> 1 + G_8(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']

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

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

(114)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']

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

(115) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_8
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 8 + 7*z

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

(116)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_8}, {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: ?, size: O(n^1) [8 + 7*z]

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

(117) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_8
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 15 + 8*z

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

(118)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + F_8(z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]

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

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

(120)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]

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

(121) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_9
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 8 + z + 7*z'

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

(122)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_9}, {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: ?, size: O(n^1) [8 + z + 7*z']

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

(123) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_9
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 16 + z + 8*z'

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

(124)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 1 }-> 1 + G_9(z, z) :|: z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 1 }-> 1 + G_9(z - 1, z') :|: z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']

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

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

(126)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']

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

(127) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: F_9
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + 8*z

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

(128)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {F_9}, {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']
  F_9: runtime: ?, size: O(n^1) [9 + 8*z]

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

(129) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: F_9
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 17 + 9*z

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

(130)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + F_9(z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']
  F_9: runtime: O(n^1) [17 + 9*z], size: O(n^1) [9 + 8*z]

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

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

(132)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 18 + 9*z' }-> 1 + s24 :|: s24 >= 0, s24 <= 8 * z' + 9, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']
  F_9: runtime: O(n^1) [17 + 9*z], size: O(n^1) [9 + 8*z]

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

(133) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: G_10
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 9 + z + 8*z'

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

(134)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 18 + 9*z' }-> 1 + s24 :|: s24 >= 0, s24 <= 8 * z' + 9, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: {G_10}
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']
  F_9: runtime: O(n^1) [17 + 9*z], size: O(n^1) [9 + 8*z]
  G_10: runtime: ?, size: O(n^1) [9 + z + 8*z']

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

(135) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: G_10
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 18 + z + 9*z'

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

(136)
Obligation:
Complexity RNTS consisting of the following rules:

   F_1(z) -{ 1 + z }-> 1 + s :|: s >= 0, s <= 0, z >= 0
   F_2(z) -{ 3 + 2*z }-> 1 + s1 :|: s1 >= 0, s1 <= z + 1, z >= 0
   F_3(z) -{ 5 + 3*z }-> 1 + s4 :|: s4 >= 0, s4 <= z + z + 2, z >= 0
   F_4(z) -{ 7 + 4*z }-> 1 + s7 :|: s7 >= 0, s7 <= z + 2 * z + 3, z >= 0
   F_5(z) -{ 9 + 5*z }-> 1 + s10 :|: s10 >= 0, s10 <= z + 3 * z + 4, z >= 0
   F_6(z) -{ 11 + 6*z }-> 1 + s13 :|: s13 >= 0, s13 <= z + 4 * z + 5, z >= 0
   F_7(z) -{ 13 + 7*z }-> 1 + s16 :|: s16 >= 0, s16 <= z + 5 * z + 6, z >= 0
   F_8(z) -{ 15 + 8*z }-> 1 + s19 :|: s19 >= 0, s19 <= z + 6 * z + 7, z >= 0
   F_9(z) -{ 17 + 9*z }-> 1 + s22 :|: s22 >= 0, s22 <= z + 7 * z + 8, z >= 0
   G_1(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 18 + 9*z' }-> 1 + s24 :|: s24 >= 0, s24 <= 8 * z' + 9, z' >= 0, z - 1 >= 0
   G_10(z, z') -{ 1 }-> 1 + G_10(z - 1, z') :|: z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z' }-> 1 + s'' :|: s'' >= 0, s'' <= 1, z' >= 0, z - 1 >= 0
   G_2(z, z') -{ 2 + z + z' }-> 1 + s2 :|: s2 >= 0, s2 <= z - 1 + 1, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + 2*z' }-> 1 + s3 :|: s3 >= 0, s3 <= z' + 2, z' >= 0, z - 1 >= 0
   G_3(z, z') -{ 4 + z + 2*z' }-> 1 + s5 :|: s5 >= 0, s5 <= z - 1 + z' + 2, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + 3*z' }-> 1 + s6 :|: s6 >= 0, s6 <= 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_4(z, z') -{ 6 + z + 3*z' }-> 1 + s8 :|: s8 >= 0, s8 <= z - 1 + 2 * z' + 3, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + z + 4*z' }-> 1 + s11 :|: s11 >= 0, s11 <= z - 1 + 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_5(z, z') -{ 8 + 4*z' }-> 1 + s9 :|: s9 >= 0, s9 <= 3 * z' + 4, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + 5*z' }-> 1 + s12 :|: s12 >= 0, s12 <= 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_6(z, z') -{ 10 + z + 5*z' }-> 1 + s14 :|: s14 >= 0, s14 <= z - 1 + 4 * z' + 5, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + 6*z' }-> 1 + s15 :|: s15 >= 0, s15 <= 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_7(z, z') -{ 12 + z + 6*z' }-> 1 + s17 :|: s17 >= 0, s17 <= z - 1 + 5 * z' + 6, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + 7*z' }-> 1 + s18 :|: s18 >= 0, s18 <= 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_8(z, z') -{ 14 + z + 7*z' }-> 1 + s20 :|: s20 >= 0, s20 <= z - 1 + 6 * z' + 7, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + 8*z' }-> 1 + s21 :|: s21 >= 0, s21 <= 7 * z' + 8, z' >= 0, z - 1 >= 0
   G_9(z, z') -{ 16 + z + 8*z' }-> 1 + s23 :|: s23 >= 0, s23 <= z - 1 + 7 * z' + 8, z' >= 0, z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  G_1: runtime: O(n^1) [z], size: O(1) [0]
  F_1: runtime: O(n^1) [1 + z], size: O(1) [1]
  G_2: runtime: O(n^1) [2 + z + z'], size: O(n^1) [1 + z]
  F_2: runtime: O(n^1) [3 + 2*z], size: O(n^1) [2 + z]
  G_3: runtime: O(n^1) [4 + z + 2*z'], size: O(n^1) [2 + z + z']
  F_3: runtime: O(n^1) [5 + 3*z], size: O(n^1) [3 + 2*z]
  G_4: runtime: O(n^1) [6 + z + 3*z'], size: O(n^1) [3 + z + 2*z']
  F_4: runtime: O(n^1) [7 + 4*z], size: O(n^1) [4 + 3*z]
  G_5: runtime: O(n^1) [8 + z + 4*z'], size: O(n^1) [4 + z + 3*z']
  F_5: runtime: O(n^1) [9 + 5*z], size: O(n^1) [5 + 4*z]
  G_6: runtime: O(n^1) [10 + z + 5*z'], size: O(n^1) [5 + z + 4*z']
  F_6: runtime: O(n^1) [11 + 6*z], size: O(n^1) [6 + 5*z]
  G_7: runtime: O(n^1) [12 + z + 6*z'], size: O(n^1) [6 + z + 5*z']
  F_7: runtime: O(n^1) [13 + 7*z], size: O(n^1) [7 + 6*z]
  G_8: runtime: O(n^1) [14 + z + 7*z'], size: O(n^1) [7 + z + 6*z']
  F_8: runtime: O(n^1) [15 + 8*z], size: O(n^1) [8 + 7*z]
  G_9: runtime: O(n^1) [16 + z + 8*z'], size: O(n^1) [8 + z + 7*z']
  F_9: runtime: O(n^1) [17 + 9*z], size: O(n^1) [9 + 8*z]
  G_10: runtime: O(n^1) [18 + z + 9*z'], size: O(n^1) [9 + z + 8*z']

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

(137) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(138)
BOUNDS(1, n^1)

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

(139) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))
Tuples:
   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
S tuples:
   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))
K tuples:none
Defined Rule Symbols:   f_0_1, f_1_1, g_1_2, f_2_1, g_2_2, f_3_1, g_3_2, f_4_1, g_4_2, f_5_1, g_5_2, f_6_1, g_6_2, f_7_1, g_7_2, f_8_1, g_8_2, f_9_1, g_9_2, f_10_1, g_10_2

Defined Pair Symbols:   F_0_1, F_1_1, G_1_2, F_2_1, G_2_2, F_3_1, G_3_2, F_4_1, G_4_2, F_5_1, G_5_2, F_6_1, G_6_2, F_7_1, G_7_2, F_8_1, G_8_2, F_9_1, G_9_2, F_10_1, G_10_2

Compound Symbols:   c, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1


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

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

(142)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))

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

   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

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

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

(144)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   F_0(z0) -> c
   F_1(z0) -> c1(G_1(z0, z0))
   G_1(s(z0), z1) -> c2(F_0(z1))
   G_1(s(z0), z1) -> c3(G_1(z0, z1))
   F_2(z0) -> c4(G_2(z0, z0))
   G_2(s(z0), z1) -> c5(F_1(z1))
   G_2(s(z0), z1) -> c6(G_2(z0, z1))
   F_3(z0) -> c7(G_3(z0, z0))
   G_3(s(z0), z1) -> c8(F_2(z1))
   G_3(s(z0), z1) -> c9(G_3(z0, z1))
   F_4(z0) -> c10(G_4(z0, z0))
   G_4(s(z0), z1) -> c11(F_3(z1))
   G_4(s(z0), z1) -> c12(G_4(z0, z1))
   F_5(z0) -> c13(G_5(z0, z0))
   G_5(s(z0), z1) -> c14(F_4(z1))
   G_5(s(z0), z1) -> c15(G_5(z0, z1))
   F_6(z0) -> c16(G_6(z0, z0))
   G_6(s(z0), z1) -> c17(F_5(z1))
   G_6(s(z0), z1) -> c18(G_6(z0, z1))
   F_7(z0) -> c19(G_7(z0, z0))
   G_7(s(z0), z1) -> c20(F_6(z1))
   G_7(s(z0), z1) -> c21(G_7(z0, z1))
   F_8(z0) -> c22(G_8(z0, z0))
   G_8(s(z0), z1) -> c23(F_7(z1))
   G_8(s(z0), z1) -> c24(G_8(z0, z1))
   F_9(z0) -> c25(G_9(z0, z0))
   G_9(s(z0), z1) -> c26(F_8(z1))
   G_9(s(z0), z1) -> c27(G_9(z0, z1))
   F_10(z0) -> c28(G_10(z0, z0))
   G_10(s(z0), z1) -> c29(F_9(z1))
   G_10(s(z0), z1) -> c30(G_10(z0, z1))

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

   f_0(z0) -> a
   f_1(z0) -> g_1(z0, z0)
   g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
   f_2(z0) -> g_2(z0, z0)
   g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
   f_3(z0) -> g_3(z0, z0)
   g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
   f_4(z0) -> g_4(z0, z0)
   g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
   f_5(z0) -> g_5(z0, z0)
   g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
   f_6(z0) -> g_6(z0, z0)
   g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
   f_7(z0) -> g_7(z0, z0)
   g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
   f_8(z0) -> g_8(z0, z0)
   g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
   f_9(z0) -> g_9(z0, z0)
   g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
   f_10(z0) -> g_10(z0, z0)
   g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

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

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

(146)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b

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

(147) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
G_1, G_2, G_3, G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(148)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_1, G_2, G_3, G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(149) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)

Induction Base:
G_1(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_1(gen_s24_31(+(1, +(n37_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c3(G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b))) ->_IH
c3(*36_31)

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

(150)
Complex Obligation (BEST)

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

(151)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_1, G_2, G_3, G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

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

(153)
BOUNDS(n^1, INF)

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

(154)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_2, G_3, G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(155) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)

Induction Base:
G_2(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_2(gen_s24_31(+(1, +(n1593_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c6(G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b))) ->_IH
c6(*36_31)

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

(156)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_3, G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(157) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)

Induction Base:
G_3(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_3(gen_s24_31(+(1, +(n4005_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c9(G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b))) ->_IH
c9(*36_31)

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

(158)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_4, G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(159) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)

Induction Base:
G_4(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_4(gen_s24_31(+(1, +(n6737_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c12(G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b))) ->_IH
c12(*36_31)

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

(160)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_5, G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(161) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)

Induction Base:
G_5(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_5(gen_s24_31(+(1, +(n9789_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c15(G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b))) ->_IH
c15(*36_31)

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

(162)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_6, G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(163) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)

Induction Base:
G_6(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_6(gen_s24_31(+(1, +(n13161_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c18(G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b))) ->_IH
c18(*36_31)

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

(164)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_7, G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(165) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)

Induction Base:
G_7(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_7(gen_s24_31(+(1, +(n16853_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c21(G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b))) ->_IH
c21(*36_31)

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

(166)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_8, G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(167) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n20865_31)

Induction Base:
G_8(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_8(gen_s24_31(+(1, +(n20865_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c24(G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b))) ->_IH
c24(*36_31)

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

(168)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)
G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n20865_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_9, G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(169) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_9(gen_s24_31(+(1, n25197_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n25197_31)

Induction Base:
G_9(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_9(gen_s24_31(+(1, +(n25197_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c27(G_9(gen_s24_31(+(1, n25197_31)), gen_s24_31(b))) ->_IH
c27(*36_31)

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

(170)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)
G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n20865_31)
G_9(gen_s24_31(+(1, n25197_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n25197_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
G_10, g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(171) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
G_10(gen_s24_31(+(1, n29849_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n29849_31)

Induction Base:
G_10(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
G_10(gen_s24_31(+(1, +(n29849_31, 1))), gen_s24_31(b)) ->_R^Omega(1)
c30(G_10(gen_s24_31(+(1, n29849_31)), gen_s24_31(b))) ->_IH
c30(*36_31)

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

(172)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)
G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n20865_31)
G_9(gen_s24_31(+(1, n25197_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n25197_31)
G_10(gen_s24_31(+(1, n29849_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n29849_31)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
g_1, g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10
----------------------------------------

(173) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
g_1(gen_s24_31(+(1, n34821_31)), gen_s24_31(b)) -> *36_31, rt in Omega(0)

Induction Base:
g_1(gen_s24_31(+(1, 0)), gen_s24_31(b))

Induction Step:
g_1(gen_s24_31(+(1, +(n34821_31, 1))), gen_s24_31(b)) ->_R^Omega(0)
b(f_0(gen_s24_31(b)), g_1(gen_s24_31(+(1, n34821_31)), gen_s24_31(b))) ->_R^Omega(0)
b(a, g_1(gen_s24_31(+(1, n34821_31)), gen_s24_31(b))) ->_IH
b(a, *36_31)

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

(174)
Obligation:
Innermost TRS:
Rules:
F_0(z0) -> c
F_1(z0) -> c1(G_1(z0, z0))
G_1(s(z0), z1) -> c2(F_0(z1))
G_1(s(z0), z1) -> c3(G_1(z0, z1))
F_2(z0) -> c4(G_2(z0, z0))
G_2(s(z0), z1) -> c5(F_1(z1))
G_2(s(z0), z1) -> c6(G_2(z0, z1))
F_3(z0) -> c7(G_3(z0, z0))
G_3(s(z0), z1) -> c8(F_2(z1))
G_3(s(z0), z1) -> c9(G_3(z0, z1))
F_4(z0) -> c10(G_4(z0, z0))
G_4(s(z0), z1) -> c11(F_3(z1))
G_4(s(z0), z1) -> c12(G_4(z0, z1))
F_5(z0) -> c13(G_5(z0, z0))
G_5(s(z0), z1) -> c14(F_4(z1))
G_5(s(z0), z1) -> c15(G_5(z0, z1))
F_6(z0) -> c16(G_6(z0, z0))
G_6(s(z0), z1) -> c17(F_5(z1))
G_6(s(z0), z1) -> c18(G_6(z0, z1))
F_7(z0) -> c19(G_7(z0, z0))
G_7(s(z0), z1) -> c20(F_6(z1))
G_7(s(z0), z1) -> c21(G_7(z0, z1))
F_8(z0) -> c22(G_8(z0, z0))
G_8(s(z0), z1) -> c23(F_7(z1))
G_8(s(z0), z1) -> c24(G_8(z0, z1))
F_9(z0) -> c25(G_9(z0, z0))
G_9(s(z0), z1) -> c26(F_8(z1))
G_9(s(z0), z1) -> c27(G_9(z0, z1))
F_10(z0) -> c28(G_10(z0, z0))
G_10(s(z0), z1) -> c29(F_9(z1))
G_10(s(z0), z1) -> c30(G_10(z0, z1))
f_0(z0) -> a
f_1(z0) -> g_1(z0, z0)
g_1(s(z0), z1) -> b(f_0(z1), g_1(z0, z1))
f_2(z0) -> g_2(z0, z0)
g_2(s(z0), z1) -> b(f_1(z1), g_2(z0, z1))
f_3(z0) -> g_3(z0, z0)
g_3(s(z0), z1) -> b(f_2(z1), g_3(z0, z1))
f_4(z0) -> g_4(z0, z0)
g_4(s(z0), z1) -> b(f_3(z1), g_4(z0, z1))
f_5(z0) -> g_5(z0, z0)
g_5(s(z0), z1) -> b(f_4(z1), g_5(z0, z1))
f_6(z0) -> g_6(z0, z0)
g_6(s(z0), z1) -> b(f_5(z1), g_6(z0, z1))
f_7(z0) -> g_7(z0, z0)
g_7(s(z0), z1) -> b(f_6(z1), g_7(z0, z1))
f_8(z0) -> g_8(z0, z0)
g_8(s(z0), z1) -> b(f_7(z1), g_8(z0, z1))
f_9(z0) -> g_9(z0, z0)
g_9(s(z0), z1) -> b(f_8(z1), g_9(z0, z1))
f_10(z0) -> g_10(z0, z0)
g_10(s(z0), z1) -> b(f_9(z1), g_10(z0, z1))

Types:
F_0 :: s -> c
c :: c
F_1 :: s -> c1
c1 :: c2:c3 -> c1
G_1 :: s -> s -> c2:c3
s :: s -> s
c2 :: c -> c2:c3
c3 :: c2:c3 -> c2:c3
F_2 :: s -> c4
c4 :: c5:c6 -> c4
G_2 :: s -> s -> c5:c6
c5 :: c1 -> c5:c6
c6 :: c5:c6 -> c5:c6
F_3 :: s -> c7
c7 :: c8:c9 -> c7
G_3 :: s -> s -> c8:c9
c8 :: c4 -> c8:c9
c9 :: c8:c9 -> c8:c9
F_4 :: s -> c10
c10 :: c11:c12 -> c10
G_4 :: s -> s -> c11:c12
c11 :: c7 -> c11:c12
c12 :: c11:c12 -> c11:c12
F_5 :: s -> c13
c13 :: c14:c15 -> c13
G_5 :: s -> s -> c14:c15
c14 :: c10 -> c14:c15
c15 :: c14:c15 -> c14:c15
F_6 :: s -> c16
c16 :: c17:c18 -> c16
G_6 :: s -> s -> c17:c18
c17 :: c13 -> c17:c18
c18 :: c17:c18 -> c17:c18
F_7 :: s -> c19
c19 :: c20:c21 -> c19
G_7 :: s -> s -> c20:c21
c20 :: c16 -> c20:c21
c21 :: c20:c21 -> c20:c21
F_8 :: s -> c22
c22 :: c23:c24 -> c22
G_8 :: s -> s -> c23:c24
c23 :: c19 -> c23:c24
c24 :: c23:c24 -> c23:c24
F_9 :: s -> c25
c25 :: c26:c27 -> c25
G_9 :: s -> s -> c26:c27
c26 :: c22 -> c26:c27
c27 :: c26:c27 -> c26:c27
F_10 :: s -> c28
c28 :: c29:c30 -> c28
G_10 :: s -> s -> c29:c30
c29 :: c25 -> c29:c30
c30 :: c29:c30 -> c29:c30
f_0 :: s -> a:b
a :: a:b
f_1 :: s -> a:b
g_1 :: s -> s -> a:b
b :: a:b -> a:b -> a:b
f_2 :: s -> a:b
g_2 :: s -> s -> a:b
f_3 :: s -> a:b
g_3 :: s -> s -> a:b
f_4 :: s -> a:b
g_4 :: s -> s -> a:b
f_5 :: s -> a:b
g_5 :: s -> s -> a:b
f_6 :: s -> a:b
g_6 :: s -> s -> a:b
f_7 :: s -> a:b
g_7 :: s -> s -> a:b
f_8 :: s -> a:b
g_8 :: s -> s -> a:b
f_9 :: s -> a:b
g_9 :: s -> s -> a:b
f_10 :: s -> a:b
g_10 :: s -> s -> a:b
hole_c1_31 :: c
hole_s2_31 :: s
hole_c13_31 :: c1
hole_c2:c34_31 :: c2:c3
hole_c45_31 :: c4
hole_c5:c66_31 :: c5:c6
hole_c77_31 :: c7
hole_c8:c98_31 :: c8:c9
hole_c109_31 :: c10
hole_c11:c1210_31 :: c11:c12
hole_c1311_31 :: c13
hole_c14:c1512_31 :: c14:c15
hole_c1613_31 :: c16
hole_c17:c1814_31 :: c17:c18
hole_c1915_31 :: c19
hole_c20:c2116_31 :: c20:c21
hole_c2217_31 :: c22
hole_c23:c2418_31 :: c23:c24
hole_c2519_31 :: c25
hole_c26:c2720_31 :: c26:c27
hole_c2821_31 :: c28
hole_c29:c3022_31 :: c29:c30
hole_a:b23_31 :: a:b
gen_s24_31 :: Nat -> s
gen_c2:c325_31 :: Nat -> c2:c3
gen_c5:c626_31 :: Nat -> c5:c6
gen_c8:c927_31 :: Nat -> c8:c9
gen_c11:c1228_31 :: Nat -> c11:c12
gen_c14:c1529_31 :: Nat -> c14:c15
gen_c17:c1830_31 :: Nat -> c17:c18
gen_c20:c2131_31 :: Nat -> c20:c21
gen_c23:c2432_31 :: Nat -> c23:c24
gen_c26:c2733_31 :: Nat -> c26:c27
gen_c29:c3034_31 :: Nat -> c29:c30
gen_a:b35_31 :: Nat -> a:b


Lemmas:
G_1(gen_s24_31(+(1, n37_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n37_31)
G_2(gen_s24_31(+(1, n1593_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n1593_31)
G_3(gen_s24_31(+(1, n4005_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n4005_31)
G_4(gen_s24_31(+(1, n6737_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n6737_31)
G_5(gen_s24_31(+(1, n9789_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n9789_31)
G_6(gen_s24_31(+(1, n13161_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n13161_31)
G_7(gen_s24_31(+(1, n16853_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n16853_31)
G_8(gen_s24_31(+(1, n20865_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n20865_31)
G_9(gen_s24_31(+(1, n25197_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n25197_31)
G_10(gen_s24_31(+(1, n29849_31)), gen_s24_31(b)) -> *36_31, rt in Omega(n29849_31)
g_1(gen_s24_31(+(1, n34821_31)), gen_s24_31(b)) -> *36_31, rt in Omega(0)


Generator Equations:
gen_s24_31(0) <=> hole_s2_31
gen_s24_31(+(x, 1)) <=> s(gen_s24_31(x))
gen_c2:c325_31(0) <=> c2(c)
gen_c2:c325_31(+(x, 1)) <=> c3(gen_c2:c325_31(x))
gen_c5:c626_31(0) <=> c5(c1(c2(c)))
gen_c5:c626_31(+(x, 1)) <=> c6(gen_c5:c626_31(x))
gen_c8:c927_31(0) <=> c8(c4(c5(c1(c2(c)))))
gen_c8:c927_31(+(x, 1)) <=> c9(gen_c8:c927_31(x))
gen_c11:c1228_31(0) <=> c11(c7(c8(c4(c5(c1(c2(c)))))))
gen_c11:c1228_31(+(x, 1)) <=> c12(gen_c11:c1228_31(x))
gen_c14:c1529_31(0) <=> c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))
gen_c14:c1529_31(+(x, 1)) <=> c15(gen_c14:c1529_31(x))
gen_c17:c1830_31(0) <=> c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))
gen_c17:c1830_31(+(x, 1)) <=> c18(gen_c17:c1830_31(x))
gen_c20:c2131_31(0) <=> c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))
gen_c20:c2131_31(+(x, 1)) <=> c21(gen_c20:c2131_31(x))
gen_c23:c2432_31(0) <=> c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))
gen_c23:c2432_31(+(x, 1)) <=> c24(gen_c23:c2432_31(x))
gen_c26:c2733_31(0) <=> c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))
gen_c26:c2733_31(+(x, 1)) <=> c27(gen_c26:c2733_31(x))
gen_c29:c3034_31(0) <=> c29(c25(c26(c22(c23(c19(c20(c16(c17(c13(c14(c10(c11(c7(c8(c4(c5(c1(c2(c)))))))))))))))))))
gen_c29:c3034_31(+(x, 1)) <=> c30(gen_c29:c3034_31(x))
gen_a:b35_31(0) <=> a
gen_a:b35_31(+(x, 1)) <=> b(a, gen_a:b35_31(x))


The following defined symbols remain to be analysed:
g_2, g_3, g_4, g_5, g_6, g_7, g_8, g_9, g_10